带有非线性边界条件的非齐次拟线性椭圆型方程组的多解性

数学物理学报 ›› 2016, Vol. 36 ›› Issue (2): 307-316.

带有非线性边界条件的非齐次拟线性椭圆型方程组的多解性

李琴¹, 杨作东^1,2

1. 南京师范大学数学科学学院南京 210023;
2. 南京师范大学教师教育学院南京 210097

收稿日期:2015-09-08 修回日期:2016-01-29 出版日期:2016-04-25 发布日期:2016-04-25
作者简介:杨作东,zdyang_jin@263.net;李琴,liqin_math@sina.com
基金资助:
国家自然科学基金(11171092,11471164)和江苏省研究生科技创新计划项目(KYZZ_0209)资助

Multiple Solutions for a Class of Quasilinear Nonhomogeneous Elliptic Systems with Nonlinear Boundary Conditions

Li Qin¹, Yang Zuodong^1,2

1 Institute of Mathematics, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023;
2 School of Teacher Education, Nanjing Normal University, Nanjing 210097

Received:2015-09-08 Revised:2016-01-29 Online:2016-04-25 Published:2016-04-25
Supported by:
Supported by the NSFC (11171092, 11471164) and Project on Graduate Students Education and Innovation of Jiangsu Province (KYZZ_0209)

摘要/Abstract

摘要：

主要研究一组带有非线性边界条件的非齐次拟线性椭圆型方程组非平凡解的存在性和多解性.利用山路引理和Ekeland变分准则,得到当λ属于特定区间时,此方程组至少存在两个非平凡解.

关键词: 存在性, 多解性, 非齐次, 非线性边界条件

Abstract:

In this paper, we study the existence and multiplicity of nontrivial solutions for a class of quasilinear elliptic systems involving nonhomogeneous nonlinearities and nonlinear boundary conditions. By using the Mountain Pass Theorem and the Ekeland's variational principle, we prove that the system has at least two nontrivial solutions when the parameter λ belongs to a certain subset of R.

Key words: Existence, Multiplicity, Nonhomogeneous, Nonlinear boundary conditions

中图分类号:

O175.2

李琴, 杨作东. 带有非线性边界条件的非齐次拟线性椭圆型方程组的多解性[J]. 数学物理学报, 2016, 36(2): 307-316.

Li Qin, Yang Zuodong. Multiple Solutions for a Class of Quasilinear Nonhomogeneous Elliptic Systems with Nonlinear Boundary Conditions[J]. Acta mathematica scientia,Series A, 2016, 36(2): 307-316.

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