变分法研究半直线上二阶微分方程由边值条件产生的多个解(英文)

Multiple Solutions for Second-order Differential Equation Generated from a Boundary Condition on the Half-line Via Variational Methods

本文讨论半直线上的一类具有非线性边值条件的二阶微分方程.利用变分法和B.Ricceri的三临界点定理得到该方程的多个正解.同时建立该方程由边值条件产生的两个解存在的充分条件.最后给出一个例子来阐释本文的结果.

In this paper, we investigate a second-order differential equation with nonlinear boundary conditions on the half-line. Multiplicity of solutions for the second-order differential equations on the half-line are considered by variational methods and a three-critical-points theorem by B. Ricceri. We also establish sufficient conditions under which such a system possesses two solutions generated from a boundary condition. To illustrate the main results,an example is given.