Positive solutions for third-order Sturm-Liouville boundary-value problems with p-Laplacian

Abstract

In this article, we consider the third-order Sturm-Liouville boundary value problem, with $p$-Laplacian, $$displaylines{ (phi_p(u''(t)))'+f(t,u(t))=0, quad tin (0,1),cr alpha u(0)-eta u'(0)=0,quad gamma u(1)+delta u'(1)=0,quad u''(0)=0, }$$ where $phi_p(s)=|s|^{p-2}s$, $p>1$. By means of the Leggett-Williams fixed-point theorems, we prove the existence of multiple positive solutions. As an application, we give an example that illustrates our result.

Keywords

• Positive solution
• Sturm-Liouville
• boundary value problem
• p-Laplacian operator
• concave functional
• fixed point