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This paper is concerned with the existence of positive homoclinic solutions for the second-order differential equation $$\begin{aligned} u^{\prime \prime }+cu^{\prime }-a(t)u+f(t,u)=0, \end{aligned}$$ where \(c\ge 0\) is a constant and the functions a and f are continuous and not necessarily periodic in t. Under other suitable assumptions on a and f, we obtain the existence of positive homoclinic solutions in both cases sub-quadratic and super-quadratic by using critical point theorems.

In this paper, we prove the paragraded version of the Wedderburn–Artin theorem. Following the methods known from the abstract case, we first prove the density theorem and observe the matrix rings whose entries are from a paragraded ring. However, in order to arrive at the desired structure theorem, we introduce the notion of a Jacobson radical of a paragraded ring and prove some properties which are analogous to the abstract case. In the process, we study the faithful and irreducible paragraded modules over noncommutative paragraded rings and prove the paragraded version of the well-known Schur lemma.

In this paper we identify the structure of complex finite-dimensional Leibniz algebras with associated Lie algebras $$sl_2^1\oplus sl_2^2\oplus \dots \oplus sl_2^s\oplus R,$$ where R is a solvable radical. The classifications of such Leibniz algebras in the cases $$\mathrm{dim} R=2, 3$$ and $$\mathrm{dim} I\ne 3$$ have been obtained. Moreover, we classify Leibniz algebras with $$L/I\cong sl_2^1\oplus sl_2^2$$ and some conditions on ideal $$I=\mathrm{id} $$ .

In this paper, we deduce the vanishing of Selmer groups for the Rankin–Selberg convolution of a cusp form with a theta series of higher weight from the nonvanishing of the associated L-value, thus establishing the rank 0 case of the Bloch–Kato conjecture in these cases. Our methods are based on the connection between Heegner cycles and p-adic L-functions, building upon recent work of Bertolini, Darmon and Prasanna, and on an extension of Kolyvagin’s method of Euler systems to the anticyclotomic setting. In the course of the proof, we also obtain a higher weight analogue of Mazur’s conjecture (as proven in weight 2 by Cornut–Vatsal), and as a consequence of our results, we deduce from Nekovař’s work a proof of the parity conjecture in this setting.

It is proved that every continuous iterative root of a piecewise monotone function with finite nonmonotonicity height, is an extension from a root on the characteristic interval. In this paper, a topological classification for those iterative roots is investigated. We first characterize all conjugacies between those piecewise monotone functions with finite nonmonotonicity height, and then determine a topological relation for their continuous iterative roots.

Let $Y$ be a fixed subset of a nonempty set $X$ and let $Fix(X,Y)$ be the set of all self maps on $X$ which fix all elements in $Y$. Then under the composition of maps, $Fix(X,Y)$ is a regular monoid. In this paper, we prove that there are only three types of maximal subsemigroups of $Fix\left(X,Y\right)$ and these maximal subsemigroups coincide with the maximal regular subsemigroups when $X\setminus Y$ is a finite set with $|X\setminus Y|\geq 2$. We also give necessary and sufficient conditions for $Fix(X,Y)$ to be factorizable, unit-regular, and directly finite.

Beer and Di Concilio [4] have given necessary and sufficient conditions for a two-sided Attouch-Wets topology to contain another on the hyperspace of non-empty closed subsets of a metrizable space as determined by metrics compatible with the topology. In the present paper, we characterize comparability of lower Attouch-Wets topologies as determined by compatible metrics.

Let R be a commutative graded ring with unity 1≠0. A proper graded ideal of R is a graded ideal I of R such that I≠R. Let ϕ:I(R)→I(R)∪{∅} be any function, where I(R) denotes the set of all proper graded ideals of R. A homogeneous element a∈R is ϕ-prime to I if ra∈I-ϕ(I) where r is a homogeneous element in R; then r∈I. An element a=∑g∈Gag∈R is ϕ-prime to I if at least one component ag of a is ϕ-prime to I. Therefore, a=∑g∈Gag∈R is not ϕ-prime to I if each component ag of a is not ϕ-prime to I. We denote by νϕ(I) the set of all elements in R that are not ϕ-prime to I. We define I to be ϕ-primal if the set P=νϕ(I)+ϕ(I) (if ϕ≠ϕ∅) or P=νϕ(I) (if ϕ=ϕ∅) forms a graded ideal of R. In the work by Jaber, 2016, the author studied the generalization of primal superideals over a commutative super-ring R with unity. In this paper we generalize the work by Jaber, 2016, to the graded case and we study more properties about this generalization.

In this paper, we introduce the notion of Saphar linear relation in a Banach space and we study the behaviour of such notion in polynomials.

Let $a,b$ be two commutative generalized Drazin invertible elements in a Banach algebra; the expressions for the generalized Drazin inverse of the product $ab$ and the sum $a+b$ were studied in some current literature on this subject. In this paper, we generalize these results under the weaker conditions $a^{2}b=aba$ and $b^{2}a=bab$. As an application of our results, we obtain some new representations for the generalized Drazin inverse of a block matrix with the generalized Schur complement being generalized Drazin invertible in a Banach algebra, extending some recent works.

In this paper we study the derived categories of coherent sheaves on Grassmannians Gr ( k , n ) , defined over the ring of integers. We prove that the category D b ( Gr ( k , n ) ) has a semi-orthogonal decomposition, with components being full subcategories of the derived category of representations of G L k . This in particular implies existence of a full exceptional collection, which is a refinement of Kapranov's collection [13] , which was constructed over a field of characteristic zero. We also describe the right dual semi-orthogonal decomposition which has a similar form, and its components are full subcategories of the derived category of representations of G L n − k . The resulting equivalences between the components of the two decompositions are given by a version of Koszul duality for strict polynomial functors. We also construct a tilting vector bundle on Gr ( k , n ) . We show that its endomorphism algebra has two natural structures of a split quasi-hereditary algebra over Z , and we identify the objects of D b ( Gr ( k , n ) ) , which correspond to the standard and costandard modules in both structures. All the results automatically extend to the case of arbitrary commutative base ring and the category of perfect complexes on the Grassmannian, by extension of scalars (base change). Similar results over fields of arbitrary characteristic were obtained independently in [7] , by different methods.

In this paper, some additive properties of the pseudo Drazin inverse are obtained in a Banach algebra. In addition, we find some new conditions under which the pseudo Drazin inverse of the sum a + b can be explicitly expressed in terms of a, az, b, bz. In particular, necessary and sufficient conditions for the existence as well as the expression for the pseudo Drazin inverse of the sum a+b are obtained under certain conditions. Also, a result of Wang and Chen [Pseudo Drazin inverses in associative rings and Banach algebras, LAA 437(2012) 1332-1345] is extended.

In this paper, we utilize Nevanlinna value distribution theory to study the uniqueness problem that a meromorphic function and its difference operator share two sets with weight $k$. Our results extend the previous results.

In this paper we establish an improvement of tilt-excess decay estimate for the Allen-Cahn equation, and use this to give a new proof of Savin’s theorem on the uniform C 1,α regularity of flat level sets. This generalizes Allard’s "-regularity theorem for stationary varifolds to the setting of Allen-Cahn equations. A new proof of Savin’s theorem on the one dimensional symmetry of minimizers in R n for n ≤ 7 is

In this paper, we establish some fixed point theorems in G-metric spaces involving generalized cyclic contractions. Some subsequent results are derived. The presented results generalize many well known results in the literature. Moreover, we provide some concrete examples and an application on the existence and uniqueness of solutions to a class of nonlinear integral equations.

The main purpose of this paper is to introduce and investigate the concepts of lacunary strong summability of order and lacunary statistical convergence of order of real-valued functions which are measurable (in the Lebesgue sense) in the interval (1,∞). Some relations between lacunary statistical convergence of order and lacunary strong summability of order are also given.

In the present paper, utilizing the techniques of suitable measures of noncompactness in Banach algebra, we prove an existence theorem for nonlinear functional-integral equation which contains as particular cases several integral and functional-integral equations that appear in many branches of nonlinear analysis and its applications. We employ the fixed point theorems such as Darbo?s theorem in Banach algebra concerning the estimate on the solutions. We also provide a nontrivial example that explains the generalizations and applications of our main result.

In this paper, we prove a Poincare inequality in Musielak–Orlicz spaces under the assumption that the Musielak function depends only on $$N-1$$ coordinates of the spatial variable x. We will use this inequality to show the existence of solutions for some elliptic inequalities with lower order terms and $$L^1$$ data in Musielak–Orlicz spaces.

In this paper we study the solvability of the generalized vector equilibrium problem (for short, GVEP) with a variable ordering relation in reflexive Banach spaces. The existence results of strong solutions of GVEPs for monotone multifunctions are established with the use of the KKM-Fan theorem. We also investigate the GVEPs without monotonicity assumptions and obtain the corresponding results of weak solutions by applying the Brouwer fixed point theorem. These results are also the extension and improvement of some recent results in the literature.

This paper provides various “contractivity” results for linear operators of the form I−C where C are positive contractions on real ordered Banach spaces X. If A generates a positive contraction semigroup in Lebesgue spaces Lp(μ), we show (M. Pierre's result) that A(λ−A)−1 is a “contraction on the positive cone”, i.e. A(λ−A)−1x≤x for all x∈L+p(μ)(λ>0), provided that p⩾2. We show also that this result is not true for 1 ⩽ p

Let G be a group with identity e. Let R be a G-graded commutative ring and M a graded R-module. In this paper, we introduce several results concerning graded semiprime submodules. And we introduce the concept of graded semi-radical of graded submodule in graded module and give a number of its properties.

Let $K$ be a complete discrete valuation field of mixed characteristic $(0,p)$ with perfect residue field. Let $(\unicode[STIX]{x1D70B}_{n})_{n\geqslant 0}$ be a system of $p$-power roots of a uniformizer $\unicode[STIX]{x1D70B}=\unicode[STIX]{x1D70B}_{0}$ of $K$ with $\unicode[STIX]{x1D70B}_{n+1}^{p}=\unicode[STIX]{x1D70B}_{n}$, and define $G_{s}$ (resp. $G_{\infty }$) the absolute Galois group of $K(\unicode[STIX]{x1D70B}_{s})$ (resp. $K_{\infty }:=\bigcup _{n\geqslant 0}K(\unicode[STIX]{x1D70B}_{n})$). In this paper, we study $G_{s}$-equivariantness properties of $G_{\infty }$-equivariant homomorphisms between torsion crystalline representations.

In this paper, we introduce and study the notions of Gorenstein n-FP-injective and Gorenstein n-flat complexes, which are special cases of Gorenstein FP-injective and Gorenstein flat complexes respectively. We prove that over a left n-coherent ring R the class of all Gorenstein n-FP-injective (resp., Gorenstein n-flat) complexes is injectively (resp., projectively) resolving and we discuss the relationship between Gorenstein n-FP-injective and Gorenstein n-flat complexes.

In the present paper we obtain some results for the asymptotic behavior of a large class of evolution families. Our approach uses the admissibility method initiated by O. Perron in the 1930's but the test functions that we choose are different from those employed in the case of differential systems.

This paper is concentrated on giving a module containment theorem for piecewise continuous almost periodic functions (pcap function for short). One first analyses the relationship between the translation number set and some Fourier exponents of a pcap function. And then, combining with Kronecker’s theorem, a module containment theorem for a pcap function is established for the first time. As an application, the module structure of a pcap solution for an impulsive differential equation is characterized. Some remarks and a corollary are given to show the advantage of the module containment theorem.

In this paper, we study dissipative q-Sturm—Liouville operators in Weyl’s limit circle case. We describe all maximal dissipative, maximal accretive, self adjoint extensions of q-Sturm—Liouville operators. Using Livšic’s theorems, we prove a theorem on completeness of the system of eigenvectors and associated vectors of the dissipative q-Sturm—Liouville operators.

In this paper, we concern the Principal Ideal Theorem (PIT) for w-Noetherian rings. Let R be a w-Noetherian ring and a be a nonzero nonunit element of R. If p is a prime ideal of R minimal over (a), then ht p ≦ 1.

In the present paper, we introduce the concepts of Prufer sheaves and adic sheaves over a weighted projective line of genus one or an elliptic curve, show that Prufer sheaves and adic sheaves can characterize the category of coherent sheaves. Moreover, we describe the relationship between Prufer sheaves and generic sheaves, and provide two methods to construct generic sheaves by using coherent sheaves and Prufer sheaves.

In this paper our aim is to study the classical Bessel-Struve kernel. Monotonicity and log-convexity properties for the Bessel-Struve kernel, and the ratio of the Bessel-Struve kernel and the Kummer confluent hypergeometric function are investigated. Moreover, lower and upper bounds are given for the Bessel-Struve kernel in terms of the exponential function and some Turan type inequalities are deduced.

In this paper we consider the nonlinear system \(\gamma _i(x_i)=\sum _{j=1}^{m}g_{ij} (x_j)\), \( 1\le i \le m\). We give sufficient conditions which imply the existence and uniqueness of positive solutions of the system. Our theorem extends earlier results known in the literature. Several examples illustrate the main result.

This paper describes the module categories for a family of generic Hecke algebras, called Yokonuma-type Hecke algebras. Yokonuma-type Hecke algebras specialize both to the group algebras of the complex reflection groups G(r,1,n) and to the convolution algebras of (B\(^{\prime }\),B\(^{\prime }\))-double cosets in the group algebras of finite general linear groups, for certain subgroups B\(^{\prime }\) consisting of upper triangular matrices. In particular, complete sets of inequivalent, irreducible modules for semisimple specializations of Yokonuma-type Hecke algebras are constructed.

In this paper, we introduce and analyze a fundamental strongly regular equivalence relation on a hypermodule over a hyperring which is the smallest equivalence relation such that the quotient is cyclic module over a (fundamental) ring. Then we state the conditions that is equivalent with the transitivity of this relation. Finally, a characterization of the derived hypermodule (with canonical hypergroup) over a Krasner hyperring has been considered.

This paper concerns mainly on various ring properties of some subrings of a skew triangular matrix ring. Necessary and sufficient conditions are obtained for a skew triangular matrix ring with constant diagonal over a ring to satisfy a certain ring property which is among being local, semilocal, semiperfect, semiregular, left quasi-duo, clean, (weakly) nil clean, exchange, uniquely (nil) clean, Hermite ring, stably finite, semiregular and I-ring. It is also proved that the projective-free property of a ring preserves by a skew triangular matrix ring with constant diagonal.

The aim of this paper is the study of surjective ideals of homogeneous polynomials between Banach spaces. To do so we define the surjective hull of a polynomial ideal and prove the main properties of this hull procedure. For a more comprehensive theory, new lifting properties of homogeneous polynomials are proved and applied to the description of the surjective hulls of the ideals of I-bounded polynomials and of composition polynomials ideals. Several applications are provided.

A semigroup (R, ·) is said to be a UA-ring if there exists a unique binary operation “+” transforming (R, ·, +) into a ring. An R-module A is said to be a UA-module if it is not possible to define a new addition in A without changing the action of R on A. In this paper we investigate topics that are related to the structure of UA-rings of endomorphisms and UA-modules over commutative Noetherian rings.

The principal aim of this paper is to study the regular and transitive subgroup functors in the universe of all finite soluble groups. We prove that they form a complemented and non-modular lattice containing two relevant sublattices. This is the answer to a question (Question 1.2.12) proposed by Skiba (1997) in the finite soluble universe.

The paper presents the generalized form of the Bernstein operator associated with any real-valued function f : [ a , b ] → ℝ {f\colon[a,b]\to\mathbb{R}} . For this generalized Bernstein operator, we study the qualitative and quantitative aspects concerning uniform convergence, order of approximation and asymptotic behavior.

In this paper, we investigate the uniform convergence of continuous linear set-valued functions on compact sets. We also consider conditions under which the family of continuous linear extensions of a differential iteration semigroup of continuous linear set-valued functions is a differentiable iteration semigroup. In particular, since the cones and normed spaces are not supposed to be complete our main results generalize some recent results on Hukuhara’s derivative of set-valued functions.

It is shown in this paper that every separably closed field with a non-trivial valuation, treated as a first-order structure in the language of valued fields, is an immediate expansion of the underlying first-order field structure; that is to say that there is no proper intermediate first-order structure between these two structures.

The aim of this paper is to relate the almost average shadowing property (ALASP) with various variants of ergodicity and with some other dynamical properties. We also study the relation of the ALASP with proximality.

This paper deals with the hyperbolic Riesz B-potential, which is the negative real power of an operator Bγ1 − ∑i = 2nBγi, where \( \begin{array}{cc}\hfill {B}_{\upgamma i}={\partial}^2/\partial {x}_i^2+\left({\upgamma}_i/{x}_i\right)\partial /\partial {x}_i,\hfill & \hfill i=1,\dots, n,\hfill \end{array} \) is a singular Bessel differential operator. We prove the boundedness of the hyperbolic Riesz B-potential in proper spaces.

The paper presents a full description of idempotent elements of the semigroup of binary relations BX(D), which are defined by semilattices of the class Σ3(X, 8). For the case where X is a finite set and Z7 = O, we derive formulas for calculating the number of idempotent elements of the respective semigroup.

Our results and examples show how transformations between self-similar sets may be continuous almost everywhere with respect to measures on the sets and may be used to carry well known notions from analysis and functional analysis, for example flows and spectral analysis, from familiar settings to new ones. The focus of this paper is on a number of surprising applications including what we call fractal Fourier analysis, in which the graphs of the basis functions are Cantor sets, discontinuous at a countable dense set of points, yet have good approximation properties. In a sequel, the focus will be on Lebesgue measure-preserving flows whose wave-fronts are fractals. The key idea is to use fractal transformations to provide unitary transformations between Hilbert spaces defined on attractors of iterated function systems.

In this paper, we establish some Hermite-Hadamard type inequalities for $(p_1,h_1)$-$(p_2,h_2)$-convex function on the co-ordinates. Furthermore, some inequalities of Hermite-Hadamard type involving product of two convex functions on the co-ordinates are also considered. The results presented here would provide extensions of those given in earlier works.

In this paper, we introduce the concept of (CLRS)-property for mappings F : X × X→X and S : X → X (wherein X stands for a partial metric space) and utilize the same to prove two common fixed point theorems for two pairs of mappings in partial metric spaces. We also furnish two examples to illustrate our main theorems.

We study some properties of the generalized local cohomology modules [Formula: see text] of [Formula: see text] with respect to a pair of ideals [Formula: see text] in Serre subcategories. Some results concerning to [Formula: see text]-cofinite modules are also given in this paper.

In the present paper, we determine the complex-valued solutions (f, g) of the functional equation $$f(x\sigma(y))+f(\tau(y)x)=2f(x)g(y),$$ in the setting of groups and monoids that need not be abelian, where \({\sigma,\tau}\) are involutive automorphisms. We prove that their solutions can be expressed in terms of multiplicative and additive functions.

The classes of right and left γ-generating matrices were introduced by D. Z. Arov in the 1980s. These matrices play an important role in the description of solutions of the indeterminate Nehari problem. In the present paper, the classes of the so-called generalized right and left γ-generating matrices, being resolvent matrices of the Nehari–Takagi problem, are introduced. For matrices of these classes, some factorization theorems are proved, and the connection between the class of generalized γ-generating matrices and the class of generalized j pq -inner matrix valued functions is found. Subclasses of singular, regular, and strongly regular generalized -generating matrices are introduced and studied.

The paper is devoted to the development of the theory of lower Q-homeomorphisms relative to a p-modulus in ℝ n , n ≥ 2. For these classes of mappings, a number of theorems on the local behavior are established, and, in particular, an analog of the famous Gehring theorem on a local Lipschitz property is proved, various theorems on estimates of distortion of the Euclidean distance are given, an estimate of the ball image measure is established, and, as a consequence, an analog of the Ikoma–Schwartz lemma is proved.

Let (X, d, μ) be a metric measure space satisfying both the geometrically doubling and the upper doubling conditions. Under the weak reverse doubling condition, the authors prove that the generalized homogeneous Littlewood–Paley g-function ġ r (r ∈ [2,∞)) is bounded from Hardy space H 1(μ) into L 1(μ). Moreover, the authors show that, if f ∈ RBMO(μ), then [ġ r (f)] r is either infinite everywhere or finite almost everywhere, and in the latter case, [ġ r (f)] r belongs to RBLO(μ) with the norm no more than ‖f‖RBMO(μ) multiplied by a positive constant which is independent of f. As a corollary, the authors obtain the boundedness of ġ r from RBMO(μ) into RBLO(μ). The vector valued Calderon–Zygmund theory over (X, d, μ) is also established with details in this paper.