The exact number of solutions for the second order nonlinear boundary value problem

Mathematica Slovaca

Peter Somora¹ 

关键词: boundary value problem;    shooting method;    shooting function;    root function;    variational solution;    variational index;   

DOI  :  10.2478/s12175-008-0086-z

学科分类：数学（综合）

来源: Slovenska Akademia Vied * Matematicky Ustav / Slovak Academy of Sciences, Mathematical Institute

【 摘 要 】

A second order nonlinear differential equation with homogeneous Dirichlet boundary conditions is considered. An explicit expression for the root functions for an autonomous nonlinear boundary value problem is obtained using the results of the paper [SOMORA, P.: The lower bound of the number of solutions for the second order nonlinear boundary value problem via the root functions method, Math. Slovaca 57 (2007), 141–156]. Other assumptions are supposed to prove the monotonicity of root functions and to get the exact number of solutions. The existence of infinitely many solutions of the boundary value problem with strong nonlinearity is obtained by the root function method as well.

【 授权许可】

Unknown