The Schauder-Tikhonov theorem in locally convex topological spaces and an extension of Krasnosel’skiĭ’s fixed point theorem due to Nashed and Wong are used to establish existence of and C solutions to Volterra and Hammerstein integral equations in Banach spaces.
In this paper we establish some results for asymptotic linear Hammerstein integral equations. Using Morse theory and in particular critical groups we prove a number of existence results.
In this paper using the projective limit approach we present new Lefschetz fixed point theorems for approximable type maps defined on PRANR’s.
Existence results are established for the resonant problem a.e. on with satisfying Dirichlet boundary conditions. The problem is singular since is a Carathéodory function, with a.e. on and .
Existence of nonnegative solutions are established for the periodic problem a.eȯn , . Here the nonlinearity satisfies a Landesman Lazer type condition.
New existence results are presented for the two point singular “resonant” boundary value problem a.eȯn with satisfying Sturm Liouville or Periodic boundary conditions. Here is the eigenvalue of a.eȯn with satisfying Sturm Liouville or Periodic boundary data.
A number of fixed point theorems are presented for weakly contractive maps which have weakly sequentially closed graph. Our results automatically lead to new existence theorems for differential inclusions in Banach spaces relative to the weak topology.
Some new fixed point results are established for mappings of the form with compact and pseudocontractive.
In this paper some new fixed point theorems of Ky Fan, Leray-Schauder and Furi-Pera type are presented for closed multifunctions.
In this paper generalized quasivariational inequalities on Fréchet spaces are deduced from new fixed point theory of Agarwal and O’Regan [1] and O’Regan [7].
In this paper we investigate the existence of solutions to impulsive problems with a -Laplacian and Dirichlet boundary value conditions. We introduce two types of solutions, namely a weak and a classical one which coincide because of the fundamental lemma of the calculus of variations. Firstly we investigate the existence of solution to the linear problem, i.e. a problem with a fixed rigth hand side. Then we use a direct variational method and next a mountain pass approach in order to get the existence...
We present a Furi-Pera type theorem for weakly sequentially continuous maps. As an application we establish new existence principles for elliptic Dirichlet problems.
The paper is concerned with existence results for positive solutions and maximal positive solutions of singular mixed boundary value problems. Nonlinearities h(t;x;y) in differential equations admit a time singularity at t=0 and/or at t=T and a strong singularity at x=0.
New fixed point results are presented for maps defined on closed subsets of a Fréchet space . The proof relies on fixed point results in Banach spaces and viewing as the projective limit of a sequence of Banach spaces.
We consider a single-species stochastic logistic model with the population's nonlinear diffusion between two patches. We prove the system is stochastically permanent and persistent in mean, and then we obtain sufficient conditions for stationary distribution and extinction. Finally, we illustrate our conclusions through numerical simulation.
This paper presents existence results for initial and boundary value problems for nonlinear differential equations in Banach spaces.
In this paper we study the existence of classical solutions for a class of abstract neutral integro-differential equation with unbounded delay. A concrete application to partial neutral integro-differential equations is considered.
We discuss the existence and multiplicity of positive solutions for a class of second order quasilinear equations. To obtain our results we will use the Ekeland variational principle and the Mountain Pass Theorem.
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