Positive solutions of second-order non-local boundary value problem with singularities in space variables

Mirosława Zima

doi:10.1186/s13661-014-0200-9

Abstract

We discuss a non-local boundary value problem of second-order, where the involved nonlinearity depends on the derivative and may be singular. The boundary conditions are given by Riemann-Stieltjes integrals. We establish sufficient conditions for the existence of positive solutions of the considered problem. Our approach is based on the Krasnoselskii-Guo fixed point theorem on cone expansion and compression.

Highlights

1 Introduction In the paper we are interested in the existence of positive solutions for the following singular non-local boundary value problem (BVP):
Some of the techniques applied to the singular BVPs are based on the fixed point theorems in cones
They established the existence of multiple positive solutions using the fixed point index technique combined with the approximation of the singular BVP ( ) by an appropriate sequence of regular BVPs

Summary

Introduction

1 Introduction In the paper we are interested in the existence of positive solutions for the following singular non-local boundary value problem (BVP): Many interesting results on the existence of solutions for the BVPs singular in the independent and/or the dependent variables can be found in the monographs [ ] and [ ] and in the recent papers; see for example [ – ] and [ ]. Some of the techniques applied to the singular BVPs are based on the fixed point theorems in cones (see [ – ] and [ ]).

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Results

Conclusion