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This paper aims to study a new class of integral equations called backward doubly stochastic Volterra integral equations (BDSVIEs, for short). The notion of symmetrical martingale solutions (SM-solutions, for short) is introduced for BDSVIEs. And the existence and uniqueness theorem for BDSVIEs in the sense of SM-solutions is established., Accept by Computers and Mathematics with Applications

This paper is concerned with the multiplicity of positive radial solutions for the weighted p -Laplacian in R n ∖ { 0 } . By constructing suitable Banach spaces, special cones and combining with the Avery–Peterson fixed point theorem, we obtain the existence of at least three positive radial solutions.

This paper is concerned with the existence of solutions for a new class of boundary value problems involving nonlinear Liouville–Caputo type fractional differential equations of arbitrary order and nonlocal multi-point and sub-strips boundary conditions. The nonlinearity depends on the unknown function as well as its lower-order fractional derivative. The existence results are obtained with the aid of Schauder type fixed point theorem and Krasnoselskii’s fixed point theorem, while the uniqueness of solutions is established by means of classical contraction mapping principle. We also discuss some variants of the given problem.

We prove a stronger version of the classic second mean value theorem for integrals.

In the this paper, we establish sufficient conditions for the existence and nonexistence of positive solutions to a general class of integral boundary value problems for a coupled system of fractional differential equations. The differential operator is taken in the Riemann–Liouville sense. Our analysis rely on Banach fixed point theorem, nonlinear differentiation of Leray–Schauder type and the fixed point theorems of cone expansion and compression of norm type. As applications, some examples are also provided to illustrate our main results.

The aim of this paper is to generalize two classical fixed point theorems given by Bogin [J. Bogin, A generalization of a fixed point theorem of Goebel, Kirk and Shimi, Canad. Math. Bull. 19 (1976) 7–12] and Greguš [M. Greguš, A fixed point theorem in Banach spaces, Boll. Un. Math. Ital. A (5) 17 (1980) 193–198]. We also complement and extend some very recent results proved by Suzuki [T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proc. Amer. Math. Soc. 136 (2008) 1861–1869].

In this paper, we consider the existence of solutions for the nonlinear fractional differential equation ^CD"0"+^@au(t)+r^CD"0"+^@a^-^1u(t)=f(t,u(t)),[email protected]?(0,1) with the boundary value conditions u(0)=u(1),u(@x)[email protected],@[email protected]?(0,1), where ^CD"0"+^@a and ^CD"0"+^@a^-^1 are the standard Caputo derivative with 1 0. By using the contraction mapping principle and the Schauder fixed point theorem, some existence results are obtained. In addition, Lemma 2.6 in this paper is a valuable tool in seeking solvability of the fractional differential equations.

The purpose of this paper is to investigate the existence and the uniqueness of symmetric positive solutions for a class of fourth-order boundary value problem: {y(4)(t)=f(t,y(t)),t∈[0,1],y(0)=y(1)=y′(0)=y′(1)=0. By using the fixed point index method, we establish the existence of at least one or at least two symmetric positive solutions for the above boundary value problem. Further, by using a fixed point theorem of general α-concave operators, we also present criteria which guarantee the existence and uniqueness of symmetric positive solutions for the above boundary value problem.

In this paper, we prove the existence and uniqueness of solutions for the boundary value problem of nonlinear impulsive differential equations of fractional order [email protected]?(1,2]. Our results are based on Altman's fixed point theorem and Leray-Schauder's fixed point theorem.

In this paper, by means of solution operator approach and contraction mapping theorem, the existence and uniqueness of mild solutions for a class of abstract delay fractional differential equations are obtained.

In this paper, we use the monotone iterative technique combined with cone theory to investigate the existence of solutions to the Cauchy problem for Caputo fractional differential equations in Banach spaces. New existence theorems are obtained for the case of a cone P being normal and fully regular respectively. Moreover, two examples are given to illustrate the abstract results.

In this paper we study the existence of mild solutions for a class of abstract fractional neutral integro-differential equations with state-dependent delay. The results are obtained by using the Leray–Schauder alternative fixed point theorem. An example is provided to illustrate the main results.

In this paper, we obtain the existence of sign-changing solutions for nonlinear second-order differential equations with integral boundary value conditions, by applying a new fixed point theorem in ordered Banach spaces, with the lattice structure derived by Liu and Sun. Our results improve on those in the literature.

In this work, we establish sufficient conditions for the existence of solutions to a general class of multi-point boundary value problems for a coupled system of fractional differential equations. The differential operator is taken in the Riemann–Liouville sense. By means of a fixed point theorem, existence results for the solutions are established. We include an example to show the applicability of our results.

We present an existence theorem for monotonic solutions of a perturbed quadratic fractional integral equation in C[0,1]. Our equation contains the famous Chandrasekhar integral equation as a special case. The concept of the measure of noncompactness related to monotonicity, introduced by J. Banas and L. Olszowy, and a fixed point theorem due to Darbo are the main tools in carrying out our proof. Moreover, we give an example for indicating the natural realizations of our abstract result presented in this paper.

In this paper, we study the n-point boundary value problems for p-Laplacian impulsive dynamic equations on time scales. By using the Leray-Schauder fixed point theorem and the nonlinear alternative of Leray-Schauder type, we get the existence of at least one positive solution. We also consider the existence of at least three positive solutions by using a new fixed point theorem. As an application, we give an example to demonstrate our results.

In this paper, we consider the existence of solutions for a class of three-point boundary value problems involving nonlinear impulsive fractional differential equations. By use of Banach’s fixed point theorem and Schauder’s fixed point theorem, some existence results are obtained.

In this paper we prove some existence results for initial and boundary value problems for functional differential inclusions of fractional order with both retarded and advanced arguments. The Banach fixed point theorem, the nonlinear alternative of the Leray–Schauder type and the Covitz–Nadler fixed point theorem are the main tools in deriving our proofs.

In this paper, by introducing τ–φ-concave operators and using the properties of cones and monotone iterative technique, some new existence and uniqueness theorems of fixed points for increasing operators with such concavity are established under more extensive conditions in ordered Banach spaces. As an application, we study the existence and uniqueness of positive solutions of generalized three-point boundary value problems for second order differential equations. The results obtained here improve and generalize many known results.

Recently, Eldred [A.A. Eldred, J. Anuradha, P. Veeramani, On equivalence of generalized multi-valued contactions and Nadler’s fixed point theorem, J. Math. Anal. Appl. (2007) doi:10.1016/j.jmaa.2007.01.087] claimed that Nadler’s [S.B. Nadler Jr., Multivalued contraction mappings, Pacific J. Math. 30 (1969) 475–488] fixed point theorem is equivalent to Mizoguchi–Takahashi’s [N. Mizoguchi, W. Takahashi, Fixed point theorems for multivalued mappings on complete metric space, J. Math. Anal. Appl. 141 (1989) 177–188] fixed point theorem. Very recently, Suzuki [T. Suzuki, Mizoguchi–Takahashi’s fixed point theorem is a real generalization of Nadler’s, J. Math. Anal. Appl. (2007) doi:10.1016/j.jmaa.2007.08.022] produced an example to disprove their claim and showed that Mizoguchi–Takahashi’s fixed point theorem is a real generalization of Nadler’s fixed point theorem. We refine/generalize Mizoguchi–Takahashi’s fixed point theorem. Our result improves a recent result by Klim and Wadowski [D. Klim, D. Wardowski, Fixed point theorems for set-valued contractions in complete metric spaces, J. Math. Anal. Appl. 334 (1) (2007) 132–139] and extends Hicks and Rhoades [T.L. Hicks, B.E. Rhoades, A banach type fixed point theorem, Math. Japonica 24 (1979) 327–330] fixed point theorem to multivalued maps.

In the present paper, we introduce the concept of @h-relaxed strong convexity of a differentiable functional and extend Ding and Yao's auxiliary variational inequality technique [X.P. Ding, J.C. Yao, Existence and algorithm of solutions for mixed quasi-variational-like inclusions in Banach spaces, Computers and Mathematics with Applications, 49 (2005), 857-869] to develop iterative algorithms for finding the approximate solutions to the mixed quasi-variational-like inclusion problem (in short, MQVLIP) in a Banach space. On the one hand, we establish a result on the existence of a solution to the equilibrium problem by virtue of well-known Brouwer's fixed-point theorem. Moreover, by using this result we derive the existence and uniqueness of a solution to the MQVLIP and the existence of the approximate solutions generated by the algorithm for the MQVLIP. On the other hand, we use the concepts of @h-relaxed strong convexity of a differentiable functional and @h-cocoercivity of a composite map to prove the strong convergence of the approximate solutions to the unique solution of the MQVLIP.

In this paper we study a non-autonomous neutral functional differential equation in a Banach space. Applying the theory of semigroups of operators to evolution equations and Krasnoselskii’s fixed point theorem we establish the existence and uniqueness of a mild almost periodic solution of the problem under consideration.

Deguire and Lassonde [P. Deguire, M. Lassonde, Familles sélectantes, Topol. Methods Nonlinear Anal. 5 (1995) 261–269] extend the concept of continuous selection and introduce the notion of selecting family for a family of set-valued mappings. In this paper, we first establish a new existence theorem of selecting families. The existence of the selecting families will be then used in order to obtain several fixed component theorems of Fan–Browder type, an intersection result, a maximal element theorem for a family of set-valued mappings and a minimax inequality.

By applying the well known Leggett–Williams multiple fixed point theorem and fixed point theorem of cone expansion and compression, this paper investigates the existence of multiple positive solutions of periodic boundary value problems for first order differential equations. Meanwhile, two examples are worked out to demonstrate the main results.

In this paper, a general hybrid fixed point theorem for the strict monotone increasing multi-valued mappings in ordered Banach spaces is proved via measure of noncompactness and it is further applied to perturbed functional nonconvex differential inclusions for proving the existence results for the extremal solutions under mixed Lipschitz, compactness and strict monotonic conditions.

We obtain a new fixed point theorem in cone, which extend the Krasnosel’skii’s compression–expansion theorem in cones. Under a quite relaxed condition two theorems for the existence of positive solutions of p-Laplacian boundary value problems are proved.

This paper is devoted to studying the existence of single and multiple positive solutions to periodic problems for first-order impulsive differential equations. In addition, we apply our existence theorems to nonlinear periodic problems with singularity at the origin. Our proofs are based on Krasnoselskii fixed-point theorem in cones.

The principle of this paper is to deal with a new existence theory for positive periodic solutions to a kind of nonautonomous functional differential equations with impulse actions at fixed moments. Easily verifiable sufficient criteria are established. The approach is based on the fixed-point theorem in cones. The paper extends some previous results and obtains some new results.

The existence theorem of Peano for the fuzzy differential equation, x′(t)=f(t,x(t)),x(t0)=x0 does not hold in general except in the special case where the fuzzy number space (En, D) is finite dimensional [1] or f is assumed to be continuous and bounded [2]. In this paper, the dissipative-type conditions which guarantee the existence theorem for Peano are specified based on the existence theorem of approximate solutions to above Cauchy problem.

This paper presents a new existence theory for single and multiple positive periodic solutions to a kind of nonautonomous Volterra integro-differential equations with impulse effects. Existence is established by using Krasnoselskii fixed-point theorem in cones. This paper extends some previous results and reports some new results about impulsive differential equation

In this paper, two multivalued versions of the well-known hybrid fixed-point theoremof Dhage [1] in Banach algebras are proved. As an application, an existence theorem for a certain differential inclusion in Banach algebras is proved.

In this paper, we establish a set of sufficient conditions for the existence of mildsolutions of nonlinear neutral integrodifferential equations in Banach spaces by using the Schaefer fixed-point theorem. An application is provided to illustrate the theory.

A new intersection theorem for multivalued maps is obtained. This new theorem requires the maps involved to satisfy a weaker compactness condition and generalizes known results. Applications of this new theorem are given to the existence of maximal and greatest elements for strict and weak relations and to minimax inequalities.

In this paper, a new fixed-point theorem of functional type in a cone is established. With using the new fixed-point theorem and imposing growth conditions on the nonlinearity, the existence of three positive solutions for the boundary value problemx″(t)+f(t,x(t),x′(t))=0,0

A set of sufficient conditions is derived for the existence of almost periodic solutions of some delay differential equations by using exponential dichotomy and fixed-point theorem. This criterion provides a method for the existence analysis of almost periodic solution of time delay systems.

This paper deals with a new existence theory for positive periodic solutions to a kind of nonautonomous functional differential equation by employing the fixed-point theorem in cones. Applying the general theorems established to several biomathematical models, the paper improves some previous results and obtains some new results.

This paper investigates the existence of global solutions for initial value problems of the nonlinear integrodifferential equations in Banach spaces. We obtain the existence of global solutions by Schauder's fixed-point theorem. Our results are the generalizations and improvements of recent results. As applications of our results, the existence of global solutions of two classes of third-order mixed boundary value problem is obtained, and an example of infinite system for nonlinear integrodifferential equations is worked out to illustrate our main results.

Sufficient conditions for existence of mild solutions for abstract second-order neutral functional integrodifferential equations are established by using the theory of strongly continuous cosine families of operators and the Schaefer theorem.

Classification and criteria for the existence of nonoscillatory solutions of nonlinear differential systems are obtained. As a consequence, the existence of positive solutions is discussed.

This paper establishes existence for semipositone (n, p) and conjugate discrete boundary value problems. Our analysis relies on Krasnoselskii's fixed-point theorem in a cone.

In this paper, the particular model that describes the thin-plate flow of incompressible non-Newtonian viscous fluids is investigated. This model, which arises from polymer processing, concerns the initial boundary problem of nonstationary thin-plate flow of non-Newtonian viscous incompressible fluids. By using monotone operator theory and Schauder's fixed-point theorem, an existence and uniqueness theorem for a generalized solution is obtained, and the regularity for this solution is tested.

The purpose of this paper is to prove new existence theorems of equilibria in generalized SSC without assuming the interior condition of the state correspondence nor the strong continuity assumption on agent's preference correspondence by using the Fan-Glicksberg fixed-point theorem, and also give some corollaries including the Nash equilibrium existence for an abstract economy. Our results generalize the corresponding results due to Keiding, Vind and Kim and Yuan in several ways.

In this paper, the Leray-Schauder nonlinear alternative is used to investigate the existence of solutions to first-order impulsive initial value problems for functional differential equations in Banach spaces. (C) 2001 Elsevier Science Ltd. All rights reserved. Computers & Mathematics with Applications

We generalize the fixed-point theorem of Leggett-Williams, which is a theorem giving conditions that imply the existence of three fixed points of an operator defined on a cone in a Banach space. We then show how to apply our theorem to prove the existence of three positive solutions to a second-order discrete boundary value problem.

This paper discusses the existence of solutions of initial value problems for n th -order nonlinear integro-differential equations of mixed type on an infinite interval in a Banach space.

In this paper, the author proves directly the equivalence between geodesic equations on a Riemannian manifold given by the Riemannian connection and the equations of motion of a unit-mass point outside of external forces on the manifold given by the priciples of least action (Section 1, Theorem 1). According to the Liouville theorem, the author gives the formulae of ratio of frequencies and periods of motion in two directions with which one can (1) distinguish periodicity or quasi-periodicity of the motion on a compact manifold determined by an integrable Hamiltonian system with two degrees of freedom; (2) obtain the period of the motion if it is periodic, if only the initial point of motion in phase space is known (Section 1, Theorem 2). As an application of Theorem 2, the geodesic flows on 2-torus and ellipsoid of three major axes of different lengths are studied (Section 2, Theorem 3; Section 3, Theorem 4). Two remarks (Section 2, Remark 1; Section 3, Remark 2) are made to discuss the extreme cases of the geodesic flows.

For the differential equations of Sobolev type we prove Picard's type existence and uniqueness theorem. Next, we formulate Euler's method and show that it is well defined on a particular ordering of the grid points. The convergence of the Euler's method is also proved.

In this paper, by using the Sadovskii fixed point theorem, we study the existence of at least one solution for the second-order three-point boundary value problem u″(t)+f(t,u(t),u′(t))=θ,0

We afford a existence criterion of positive solutions of a boundary value problem concerning a second order functional differential equation by using the Krasnoselskii fixed point theorem on cones in Banach spaces. Moreover, we also apply our results to establish several existence theorems of multiple positive solutions for some functional differential equations.

In this paper, by using fixed point theory and a new method, we study the existence and uniqueness of solutions of initial value problems for nonlinear fractional differential equations and neutral differential equations with infinite delay and obtain two new existence and uniqueness results.