一类非线性二阶Robin问题多个正解的存在性

Multiplicity of Solutions for a Class of Nonlinear Second-Order Robin Problems

摘要:

本文利用不动点指数理论证明了一类非线性二阶~Robin~问题 $$ \left\{\begin{array}{ll} u''(t)-k^{2}u(t)+\lambda f(u(t))=0, ~~\ \ \ t\in (0,1),~~k\neq0,\\[2ex] u'(0)=0,~~u(1)=0 \end{array} \right. $$ 多个正解的存在性,~其中~$f:[0,\infty)\rightarrow [0,\infty)$~为连续函数且有多个零点,~$\lambda >0$~为参数.

Abstract:

In this paper,~we use the fixed point index theory to show the existence of multiple positive solutions for a class of second-order Robin problems $$ \left\{\begin{array}{ll} u''(t)-k^{2}u(t)+\lambda f(u(t))=0, ~~\ \ \ t\in (0,1),~~k\neq0,\\[2ex] u'(0)=0,~~u(1)=0 \end{array} \right. $$ where~$f:[0,\infty)\rightarrow [0,\infty)$~is continuous and has multiple zeros,~$\lambda >0$~is a parameter.