LIU Chunhan.Multiple solutions for a class of p-Laplacian elliptic equations[J].Journal of Yanbian University,2018,44(03):194-198.
一类 p -拉普拉斯椭圆方程的多重解
- Title:
- Multiple solutions for a class of p-Laplacian elliptic equations
- 关键词:
- 局部环绕; 临界点定理; p-拉普拉斯椭圆方程; 非平凡解
- Keywords:
- local linking; critical point theorem; p-Laplacian elliptic equations; nontrivial solutions
- 分类号:
- O175.25
- 文献标志码:
- A
- 摘要:
- 利用局部环绕的临界点定理,在没有使用 Ambrosetti-Rabinowitz型增长条件下,讨论了一类 p-拉普拉斯椭圆方程,获得了方程的多个非平凡解.所得结果改进和推广了文献[5-7]中的相关结论.
- Abstract:
- Using critical point theorem related to local linking, the p-Laplacian elliptic equations are discussed without using Ambrosetti-Rabinowitz type growth conditions, and some nontrivial solutions are obtained. The results extend and improve the relevant conclusion in the literature [5-7].
参考文献/References:
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[2] Perera K, Szulkin A. p-Laplacian problems where the nonlinearity crosses an eigenvalue[J]. Discrete Contin Dyn Syst, 2005,13:743-753.
[3] Degiovanni M, Lancelotti S. Linking over cones and nontrivial solutions for p-Laplace equations with p-superlinear nonlinearity[J]. Ann Inst H Poincare Anal Non Lineaire, 2007,24:907-919.
[4] Liu J, Su J. Remark on multiple nontrivial solutions for quasi-linear resonant problem[J]. J Math Anal Appl, 2001,258:209-222.
[5] Jiu Q, Su J. Existence and multiplicity results for Dirichlet problems with p-Laplacian[J]. J Math Anal Appl, 2003,281:587-601.
[6] Ou Z, Li C, Yuan J. Multiplicity of nontrivial solutions for quasilinear elliptic equation[J]. J Math Anal Appl, 2012,388:198-204.
[7] Liu D, Zhao P. Multiple nontrivial solutions to a p-Kirchhoff equation[J]. Nonlinear Anal, 2012,75:5032-5038.
[8] Frigon M. On a new notion of linking and application to elliptic problems at resonance[J]. J Differential Equations, 1999,153(1):96-120.
[9] Brezis H, Nirenberg L. Remarks on finding critical points[J]. Comm Pure Appl Math, 1991,44:939-963.
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备注/Memo
收稿日期: 2018-06-21
作者简介: 刘春晗(1981—),男,副教授,研究方向为非线性泛函分析及其应用.
基金项目: 山东省自然科学基金资助项目(ZR2016AB04); 齐鲁师范学院青年教师科研基金资助项目(2016L0603)