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.

Admissibility is a technical condition that ensures that the fixed point index of the flow is well-defined [Gor06]. Recall that a flow is admissible if and only if it is upper semicontinuous (i.e. if the limit of a convergent sequence of trajectories is a trajectory) and if there exists h > 0 such that, for any point x, the set of trajectory segments S(x,h) starting at x and defined on the time...

*Correspondence: [email protected] 1School of Mathematics and Physics, Changzhou University, Changzhou, 213164, China 2College of Science, Hohai University, Nanjing, 210098, China Full list of author information is available at the end of the article Abstract In this paper we compute the fixed point index for A-proper semilinear operators under certain boundary conditions. The proof is based ...

In this paper, we study the existence of positive radial solutions for the elliptic system by fixed point index theory. AMS subject classification: 34B15, 45G15.

In this article, we study a class of boundary value problems with p-Laplacian. By using a “Green-like” functional and applying the fixed point index theory, we obtain eigenvalue criteria for the existence of positive solutions. Several explicit conditions are derived as consequences, and further results are established for the multiplicity and nonexistence of positive solutions. Extensions are ...

This paper investigates the existence and multiplicity of positive solutions for a second-order delay p-Laplacian boundary value problem. By using fixed point index theory, some new existence results are established.

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.

Let p be a saddle fixed point for an orientation-preserving surface diffeomorphism f , admitting a homoclinic point p. Let V be an open 2-cell bounded by a simple loop formed by two arcs joining p to p, lying respectively in the stable and unstable curves at p. It is shown that f |V has fixed point index ρ ∈ {1, 2} where ρ depends only on the geometry of V near p. More generally, for every n ≥ ...

In this paper, by employing fixed point index theory and Leray-Schauder degree theory, we obtain the existence and multiplicity of sign-changing solutions for nonlinear second-order differential equations with integral boundary value conditions.

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