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...

Recommended by Kanishka Perera Using fixed point index theory, we obtain several sufficient conditions of existence of at least one positive solution for third-order m-point boundary value problems.

Given an orientation-preserving homeomorphism of the plane, a rotation number can be associated with each locally attracting fixed point. Assuming that the homeomorphism is dissipative and the rotation number vanishes we prove the existence of a second fixed point. The main tools in the proof are Carathéodory prime ends and fixed point index. The result is applicable to some concrete problems i...

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.

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.

Let P be cone Banach space E, A, K are two mappings in P, A accretive, K s k-set contraction, then fixed point index defined for mapping -A+K, some fixed point theorems are also deduced.

Recently, periodic boundary value problems PBVPs for short for dynamic equations on time scales have been studied by several authors by using the method of lower and upper solutions, fixed point theorems, and the theory of fixed point index. We refer the reader to 1–10 for some recent results. In this paper we are interested in the existence of positive solutions for the following first-order P...

In this paper, by using the classical fixed-point index theorem for compact maps and Leggett-Williams fixed point theorem, some sufficient conditions for the existence of multiple positive solutions for a class of second-order p-Laplacian boundary value problem with impulse on time scales are established. We also give an example to illustrate our results

In this paper, we study a generalized Sturm-Liouville boundaryvalue problems with two positive parameters. By constructing a completely continuous operator and combining fixed point index theorem and some properties of the eigenvalues of linear operators, we obtain sufficient conditions for the existence of at least one positive solution.

An index theory is presented for compact absorbing contractive Jc or SJc maps and several new fixed point theorems are given for such maps. AMS(MOS) subject classification: 47H10