Using the theory of the fixed point index in a cone and the LeraySchauder degree, this paper investigates the existence and multiplicity of nontrivial solutions for a class of fourth order m-point boundary-value problems.

Using the theory of fixed point theorem in cone, this paper presents the existence of positive solutions for the singular m-point boundary value problem

In this paper, we obtain new existence results for multiple positive solutions of a delay singular differential boundary-value problem. Our main tool is the fixed point index method.

By means of calculation of the fixed point index in cone we consider the existence of one or two positive solutions for the fourth-order boundary value problem with variable parameters { u(t) + B(t)u′′(t)−A(t)u(t) = f(t, u(t), u′′(t)), 0 < t < 1, u(0) = u(1) = u′′(0) = u′′(1) = 0, where A(t), B(t) ∈ C[0, 1] and f(t, u, v) : [0, 1]× [0,∞)×R → [0,∞) is continuous.

This paper studies the existence of positive solutions for a class of second-order semipositone differential equations with a negatively perturbed term and integral boundary conditions. By using a well-known fixed-point index theorem, some new existence results are derived for the case where nonlinearity is allowed to be sign changing. Several examples are presented to demonstrate the applicati...

In this article, we consider nonlocal p-Laplacian boundary-value problems with integral boundary conditions and a non-negative real-valued boundary condition as a parameter. The main purpose is to study the existence, nonexistence and multiplicity of positive solutions as the boundary parameter varies. Moreover, we prove a sub-super solution theorem, using fixed point index theorems.

We study the covering dimension of (positive ) solutions to varoius classes of nonlinear equations based on the nontriviality of the fixed point index of a certain condensing map. Applications to semilinear equations and to nonlinear perturbations of the Wiener-Hopf integral equations are given.

Based on the fixed point index theory for a Banach space, nontrivial periodic solutions are found for a class of integral equation of the form φ(x) = Z [x,x+ω]∩Ω K(x, y)f(y, φ(y − τ(y))) dy, x ∈ Ω, where Ω is a closed subset of RN with perioidc structure. Nonlinear Hammerstein integral equations of the form

We apply topological methods to the study of the set of harmonic solutions of periodically perturbed autonomous ordinary differential equations on differentiable manifolds, allowing the perturbing term to contain a fixed delay. In the crucial step, in order to cope with the delay, we define a suitable (infinite dimensional) notion of Poincaré T -translation operator and prove a formula that, in...

The existence of nonzero solutions for a class of generalized variational inequalities is studied by fixed point index approach for multivalued mappings in finite dimensional spaces and reflexive Banach spaces. Some new existence theorems of nonzero solutions for this class of generalized variational inequalities are established.