Search

Abstract: We introduce a cyclic generalized -weakly contractive mappings for a map in a metric space and originate existence and uniqueness results of fixed points for such mappings. Examples are given to support the usability of our results. At the end of the results, an application to the study of existence and uniqueness of solutions for a class of nonlinear integral equations is presented. [Copyright &y& Elsevier]

Abstract: In the present work, a non-local boundary value problem with special gluing conditions for a mixed parabolic–hyperbolic equation with parameter is considered. The parabolic part of this equation is a fractional analogue of heat equation and the hyperbolic part is the telegraph equation. The considered problem is reduced, for positive values of the parameter, to an equivalent system of the second kind Volterra integral equations. Due to the influence of the fractional diffusion equation, the looked for solution belongs to a specific class of functions. The method of the Green functions and the properties of integro-differential operators are on the basis of the investigation. [Copyright &y& Elsevier]

Abstract: In this paper, we extend the coupled fixed point theorems for mixed monotone operators obtained by Bhaskar and Lakshmikantham [T.G. Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. 65 (2006) 1379–1393] and Luong and Thuan [N.V. Luong and N.X. Thuan, Coupled fixed points in partially ordered metric spaces and application, Nonlinear Anal. 74 (2011) 983–992], by weakening the involved contractive condition. An example as well as an application to nonlinear Fredholm integral equations is also given in order to illustrate the effectiveness of our generalizations. [Copyright &y& Elsevier]

Abstract: The statements on solvability, solution estimates, and well-posedness of equations with conditionally covering mappings are proved. The results obtained are applied to the investigation of Volterra equations (including integral equations) unsolved for the unknown function. [Copyright &y& Elsevier]

Abstract: In this paper, we prove existence, uniqueness and comparison results for solutions of differential and integral equations in Banach spaces containing Henstock–Kurzweil integrable functions from a compact real interval to an ordered Banach space. [Copyright &y& Elsevier]

Abstract: In this paper we consider the asymptotic stability of a generalized linear neutral differential equation with variable delays by using the fixed point theory. An asymptotic stability theorem with a necessary and sufficient condition is proved, which improves and generalizes some results due to Burton (2003) , Zhang (2005) , Raffoul (2004) , and Jin and Luo (2008) . Two examples are also given to illustrate our results. [Copyright &y& Elsevier]

Abstract: The purpose of this paper is to present some coupled fixed point theorems for a mixed monotone operator in a complete metric space endowed with a partial order by using altering distance functions. We also present an application to integral equations. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we prove some coupled fixed point theorems for mappings having a mixed monotone property in partially ordered metric spaces. The main results of this paper are generalizations of the main results of Bhaskar and Lakshmikantham [T. Gnana Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. TMA 65 (2006) 1379–1393]. As an application, we discuss the existence and uniqueness for a solution of a nonlinear integral equation. [Copyright &y& Elsevier]

Abstract: In this paper, we introduce the -concave–convex operator. Without any compact or continuous assumptions, we prove the existence and uniqueness of fixed points, giving monotone iterative sequences for the unique fixed point for the operator. Finally, we apply the results to an integral equation of polynomial type which possesses items of measurable functions. [Copyright &y& Elsevier]

Abstract: We consider a nonlinear optimal control problem with an integral equation as the control object, subject to control constraints. This integral equation corresponds to the fractional moment of a stochastic process involving short-range and long-range dependences. For both cases, we derive the first-order necessary optimality conditions in the form of the Euler–Lagrange equation, and then apply them to obtain a numerical solution of the problem of optimal portfolio selection. [Copyright &y& Elsevier]

Abstract: By the use of a Guo–Krasnoselskii theorem in cones, existence of positive eigenvalues yielding nonnegative or positive solutions to an integral equation is studied. The results are applied to a variety of boundary value problems concerning ordinary differential equations. [Copyright &y& Elsevier]

Abstract: We study integral equations corresponding to some quasilinear equations with nonlinearities of Lane–Emden and Hartree type. Regularity, symmetry, and uniqueness of these equations are considered. We obtain the uniqueness of the ground state of critical Hartree equation and extend the moving plane method of integral equation in [W. Chen, C. Li, B. Ou, Classification of solutions for an integral equation, Comm. Pure Appl. Math. LIX (2006) 0330–0343; W. Chen, C. Li, B. Ou, Classification of solutions for a system of integral equations, Comm. Partial Differential Equations 30 (1–3) (2005) 59–65] to some integral equations corresponding to the -Laplace equation. We use ideas from the potential theories for the -Laplace equations and Hessian equations. [Copyright &y& Elsevier]

Abstract: A general approach is presented for proving existence and uniqueness of solutions to the singular boundary value problem The proof is constructive in nature, and could be used for numerical generation of the solution. The only restriction placed on is that it not be a singular function of the independent variable ; singularities in are easily avoided. Solutions are found in finite regions where , using an integral equation whose Green’s function contains an adjustable parameter that secures convergence of the Picard iterative sequence. Methods based on the theory are developed and applied to a set of problems that have appeared previously in published works. [Copyright &y& Elsevier]

Abstract: In this paper we prove dominated and monotone convergence theorems for HL integrable Banach-valued functions. These results and a fixed point theorem in ordered spaces are then applied to prove existence and comparison results for integral equations of Fredholm type in ordered Banach spaces involving Kurzweil integrals or improper integrals. Results are used also to solve concrete second-order functional boundary value problems involving discontinuities and singularities. [Copyright &y& Elsevier]

Abstract: We present new blow-up theorems, which are only in terms of the ordinary limit, for the solutions to the Cauchy problem for integral equations with infinite delay in Banach spaces. Moreover, we provide an example to illustrate our abstract result. [Copyright &y& Elsevier]