Existence of positive solutions for self-adjoint boundary-value problems with integral boundary conditions at resonance

Abstract

In this article, we study the self-adjoint second-order boundary-value problem with integral boundary conditions, $$displaylines{ (p(t)x'(t))'+ f(t,x(t))=0,quad tin (0,1),cr p(0)x'(0)=p(1)x'(1),quad x(1)=int_0^1x(s)g(s)ds, }$$ which involves an integral boundary condition. We prove the existence of positive solutions using a new tool: the Leggett-Williams norm-type theorem for coincidences.

Keywords

• Boundary value problem
• resonance
• cone
• positive solution
• coincidence