Positive solutions for singular nonlinear beam equation

Abstract

In this paper, we study the existence of solutions for the singular p-Laplacian equation $$displaylines{ ig(|u''|^{p-2}u''ig)''-f(t,u)=0,quad tin (0,1) cr u(0)=u(1)=0, cr u''(0)=u''(1)=0, }$$ where $f(t,u)$ is singular at $t=0,1$ and at $u=0$. We prove the existence of at least one solution.

Keywords

• p-laplacian
• singular
• fixed point theorem.