Global structure of one-sign solutions for a simply supported beam equation

Abstract

Abstract In this paper, we consider the nonlinear eigenvalue problem u ′′′′ = λ h ( t ) f ( u ) , 0 0 $sf(s)>0$ for s ≠ 0 $s\neq0$ , and f 0 = f ∞ = 0 $f_{0}=f_{\infty}=0$ , f 0 = lim | s | → 0 f ( s ) / s $f_{0}=\lim_{|s|\rightarrow0}f(s)/s$ , f ∞ = lim | s | → ∞ f ( s ) / s $f_{\infty}=\lim_{|s|\rightarrow\infty}f(s)/s$ . We investigate the global structure of one-sign solutions by using bifurcation techniques.

Keywords

• Connected component
• Green function
• One-sign solutions
• Bifurcation
• Simply supported beam