摘要
p-Laplacian方程是一类比较重要的微分方程模型,它来自于非牛顿流体问题及非线性弹性问题.在比Ambrosetti-Rabinowitz条件更弱的局部超线性条件下,研究含有Hardy位势的p-Laplacian方程Dirichlet边值问题解的存在性.通过将这类问题的解转化为定义在一个适当空间上泛函的临界点,然后利用Hardy不等式和临界点理论中的对称山路建立了无穷多解存在的充分条件,所得结论推广和改进了已知结果,并举例说明了所获得的主要结果是有效的.
p-Laplacian equation is an important model of differential equation from non-Newtonian fluid theory.and nonlinear elasticity.In this paper,we investigate the existence of infinitely many solutions for Dirichlet boundary value problem of p-Laplician equation with Hardy potential under a condition weaker than Ambrosetti-Rabinowitz＇ s local superlinear condition.We convert solutions of this problem into the critical points of a functional defined on a proper space,and some sufficient conditions for the existence of infinitely many solutions are obtained by the Hardy inequality and sysmmetric mountain pass theorem in critical point theory.The results generalize and improve the existing ones.An illustrative example is given to demonstrate the effectiveness of the obtained main result.
出处
《四川师范大学学报（自然科学版）》
CAS
CSCD
北大核心
2013年第6期836-840,共5页
Journal of Sichuan Normal University（Natural Science）
基金
国家自然科学基金(11161041)资助项目
