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The existence of at least two solutions to superlinear integral equation in cone is proved using the Krasnosielskii Fixed Point Theorem. The result is applied to the Dirichlet BVPs with the fractional Laplacian.
In this paper, we discuss the existence of local strong solutions for the multivalued version of three-dimensional nonstationary Navier-Stokes equation in Banach spaces. Also, we considered a more general inclusion problem and studied the…
In this paper, we investigate the existence and uniqueness of fixed point for partially ordered contraction type operators in Banach Space. We also present applications to integral and differential equations.
This article presents a deep investigation of fixed points for multivalued weak contractions in cone metric spaces. We extend Berinde weak contraction principles to the multivalued setting in cone metric spaces, developing existence,…
The objective of this paper is to introduce and study a complicated nonlinear system, called coupled variational-hemivariational inequalities, which is described by a highly nonlinear coupled system of inequalities on Banach spaces. We…
Local indices at isolated fixed points of a differentiable compact nonlinear map $T$ on Banach spaces will be discussed. These results are applied to establish the existence of nontrivial solutions. As an example, the existence of…
It is well known that fixed point problems of contractive-type mappings defined on cone metric spaces over Banach algebras are not equivalent to those in usual metric spaces (see [3] and [10]). In this framework, the novelty of the present…
We study the existence of nonnegative solutions for a system of impulsive differential equations subject to nonlinear, nonlocal boundary conditions. The system presents a coupling in the differential equation and in the boundary conditions.…
We consider the boundary value problems (BVPs) for linear secondorder ODEs with a strongly positive operator coefficient in a Banach space. The solutions are given in the form of the infinite series by means of the Cayley transform of the…
In this paper, we prove several fixed point theorems on both of normal partially ordered Banach spaces and regular partially ordered Banach spaces by using the normality, regularity, full regularity, and chain -complete property. Then, by…
In this paper, we establish some new variants of fixed point theorems for a large class of countably nonexpansive multi-valued mappings. Some fixed point theorems for the sum and the product of three multi-valued mappings defined on…
In this article, we propose an idea to develop some sufficient conditions for the existence and uniqueness of a positive definite common solution to a pair of non-linear matrix equations. To proceed this, we present some interesting common…
In the paper, results on the existence of critical points in annular subsets of a cone are obtained with the additional goal of obtaining multiplicity results. Compared to other approaches in the literature based on the use of…
We present the bilinear forms of the (continuous) Painlev\'e equations obtained from the continuous limit of the analogous expresssions for the discrete ones. The advantage of this method is that it leads to very symmetrical results. A new…
This paper addresses the study of novel constructions of variational analysis and generalized differentiation that are appropriate for characterizing robust stability properties of constrained set-valued mappings/multifunctions between…
We study the existence of positive solutions on the half-line of a second order ordinary differential equation subject to functional boundary conditions. Our approach relies on a combination between the fixed point index for operators on…
In this paper, we study a new iterative method for a common fixed point of a finite family of Bregman strongly nonexpansive mappings in the frame work of reflexive real Banach spaces. Moreover, we prove the strong convergence theorem for…
In this work we will consider integral equations defined on the whole real line and look for solutions which satisfy some certain kind of asymptotic behavior. To do that, we will define a suitable Banach space which, to the best of our…
We prove the existence of multiple signed bounded solutions for a quasilinear elliptic equation with concave and convex nonlinearities. For this, we use a variational approach in an intersection Banach space indroduced by Candela and…
Set differential equations are usually formulated in terms of the Hukuhara differential, which implies heavy restrictions for the nature of a solution. We propose to reformulate set differential equations as ordinary differential equations…