研究了一类具有非光滑局部Lipschitz位势(半变分不等式)的非线性特征值问题
其中 1 <
p < ∞,Ω ⊂ R
N是有界区域.目的是把最近的超线性(即
p = 2)问题的非平凡解存在性和连续性结果推广到一般情况 (即 1 <
p <∞).不仅推广了 Miyagaki and Souto 研究工作[Superlinear Problems without Ambrosetti and Rabinowitz Growth Condition,
Jour.Diff.Equa.,245 (2008) 3628-3638],同时也推广了Schechter和 Zou 的研究工作 [Superlinear Problems,
Pacific J.Math.,214 (2004) 145-160].本文使用的方法基于局部Lipschitz函数的非光滑临界点理论.
Abstract
We consider a kind of nonlinear eigenvalue problem driven by the p-laplacian with a nonsmooth locally Lipschitz potential (hemivariational inequality), that is,
where 1 <
p < ∞, and Ω ⊂ R
N is a bounded domain. The purpose of this paper is to extend earlier existence and continuation results of nontrivial solutions of the problem in the superline case (i.e.,
p = 2) to the general case (i.e., 1 <
p < ∞). We not only extend the existence results of nontrivial solutions for almost every parameter λ due to Miyagaki and Souto [Superlinear Problems without Ambrosetti and Rabinowitz Growth Condition,
Jour. Diff. Equa., 245 (2008) 3628-3638], but also extend the existence results of nontrivial solutions for every parameter λ due to Schechter and Zou [Superlinear Problems,
Pacific J. Math., 214 (2004) 145-160] to the general case when 1 <
p < ∞. Our approach is based on the non-smooth critical point theory for locally Lipschitz functions.
关键词
p-Laplacian /
非线性特征值问题 /
超线性问题 /
变分方法
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Key words
p-Laplacian /
nonlinear eigenvalue problem /
superlinear problems /
variational method
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参考文献
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脚注
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基金
国家自然科学基金(11126286,10971043,11001063);中央高校基本科研业务费专项资金(20111134);中国博士后基金(20110491032);黑龙江省杰出青年基金(JC200810);省自然科学基金(A200803)
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