Multiplicity of nodal solutions for fourth order equation with clamped beam boundary conditions

Abstract

In this paper, we study the global structure of nodal solutions of $$ \begin{cases} u''''(x)=\lambda h(x)f(u(x)), & 0 0$ is a parameter, $h\in C([0,1],(0, \infty))$, $f\in C(\mathbb{R})$ and $sf(s)>0$ for $|s|>0$. We show the existence of $S$-shaped component of nodal solutions for the above problem. The proof is based on the bifurcation technique.

Keywords

• clamped beam
• fourth order equations
• connected component
• nodal solutions
• bifurcation