一类超线性p(x)-调和方程的无穷多解

J4 ›› 2012, Vol. 47 ›› Issue (10): 116-120.

一类超线性p(x)-调和方程的无穷多解

张申贵

西北民族大学数学与计算机科学学院, 甘肃兰州 730030

收稿日期:2011-11-05 出版日期:2012-11-20 发布日期:2012-10-26
作者简介:张申贵(1980- ), 男, 讲师, 研究方向为非线性泛函分析. Email: zhang.sg@tom.com
基金资助:
中央高校基本科研业务费专项资助(ZYZ2011078);西北民族大学校中青年科研项目(12XB38)

Infinitely many solutions for a class of superlinear p(x)-biharmonic equation

ZHANG Shen-gui

College of Mathematics and Computer Science, Northwest University for Nationalities, Lanzhou 730030, Gansu, China

Received:2011-11-05 Online:2012-11-20 Published:2012-10-26

摘要/Abstract

摘要：

p(x)-调和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。该文利用临界点理论研究p(x)-调和方程解的存在性。在比Ambrosetti-Rabinowitz条件更弱的超线性条件下,得到了无穷多解存在的充分条件, 所得结论推广了已知结果。

关键词: p(x)-调和方程; 超线性; 临界点

Abstract:

P(x)-biharmonic 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 p(x)-biharmonic equation by critical point theory. Under a condition weaker than Ambrosetti-Rabinowitz′s superlinear condition, some sufficient conditions for the existence of infinitely many solutions are obtained, and results improve the existing ones.

Key words: p(x)-biharmonic equation; superlinear; critical point

张申贵. 一类超线性p(x)-调和方程的无穷多解[J]. J4, 2012, 47(10): 116-120.

ZHANG Shen-gui. Infinitely many solutions for a class of superlinear p(x)-biharmonic equation[J]. J4, 2012, 47(10): 116-120.

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