Author:
Yan Dongliang,Ma Ruyun,Su Xiaoxiao
Abstract
AbstractIn this paper, we consider the nonlinear eigenvalue problem
$$\begin{gathered} u''''= \lambda h(t)f(u),\quad 0< t< 1, \\ u(0)=u(1)=u''(0)=u''(1)=0, \\ \end{gathered} $$u′′′′=λh(t)f(u),0<t<1,u(0)=u(1)=u″(0)=u″(1)=0, where $h\in C([0,1], (0,\infty))$h∈C([0,1],(0,∞)); $f\in C(\mathbb{R},\mathbb{R})$f∈C(R,R) and $sf(s)>0$sf(s)>0 for $s\neq0$s≠0, and $f_{0}=f_{\infty}=0$f0=f∞=0, $f_{0}=\lim_{|s|\rightarrow0}f(s)/s$f0=lim|s|→0f(s)/s, $f_{\infty}=\lim_{|s|\rightarrow\infty}f(s)/s$f∞=lim|s|→∞f(s)/s. We investigate the global structure of one-sign solutions by using bifurcation techniques.
Funder
National Natural Science Foundation of China
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Discrete Mathematics and Combinatorics,Analysis