[1]熊辉,杨光.含凹凸非线性的p(x)-Laplace方程多正解的存在性[J].江西师范大学学报(自然科学版),2014,(03):254-257.
　XIONG Hui,YANG Guang.The Existence of Multiple Positive Solutions for the p(x)-Laplacian Equation with Concave and Convex Nonlinearities[J].Journal of Jiangxi Normal University:Natural Science Edition,2014,(03):254-257.
点击复制

含凹凸非线性的p(x)-Laplace方程多正解的存在性()
分享到：

《江西师范大学学报》（自然科学版）[ISSN:1006-6977/CN:61-1281/TN]

卷:
期数:
2014年03期
页码:
254-257
栏目:
出版日期:
2014-06-30

文章信息/Info

Title:
The Existence of Multiple Positive Solutions for the p(x)-Laplacian Equation with Concave and Convex Nonlinearities
作者:
熊辉;杨光
东莞理工学院数学教研室,广东 东莞,523808
Author(s):
XIONG Hui；YANG Guang
关键词:
凹凸非线性; 正解存在性; 山路原理; Ekeland变分原理
Keywords:
concave and convex nonlinearity; existence of positive solutions; mountain pass theorem; Ekeland varia-tional principle
分类号:
O175.24；O411.3
文献标志码:
A
摘要:
利用基于临界点理论的变分方法和Ekeland变分原理，研究含凹凸非线性的参数型p（ x）-Laplace方程的Dirichlet问题的正解的存在性。在该方程中，超线性项不需要满足Ambrosetti-Rabinowitz条件，对于取值较小的参数，证明了所研究的问题至少有2个非平凡的光滑正解。
Abstract:
Using variational methods based on the critical point theory and the Ekeland variational principle,a non-linear parametric Dirichlet problem,driven by the anisotropic p( x)-Laplacian with the combined effects of concave and convex terms,is studied. In this problem,the superlinear nonlinearity does not need to satisfy the Ambrosetti-Rabinowitz condition. It is shown that for small values of the parameter,the problem has at least two nontrivial smooth positive solutions.

参考文献/References:

[1] Ambrosetti A,Brézis H,Cerami G.Combined effects of concave and convex nonlinearities in some elliptic problems [J].J Funct Anal,1994,122(2):519-543.
[2] 张申贵.局部超线性常微分p-Laplacian系统的多重周期解 [J].江西师范大学学报:自然科学版,2013,37(3):240-243.
[3] García Azorero J,Manfredi J,Peral Alonso I.Sobolev versus Hölder local minimizers and global multiplicity for some quasilinear elliptic equations [J].Commun Contemp Math,2000,2(3):385-404.
[4] Guo Zongming,Zhang Zhitao.W versus C local minimizers and multiplicity results for quasilinear elliptic equations [J].J Math Anal Appl,2003,286(1):32-50.
[5] Lü Dengfeng,Xiao Jianhai,Xu Guojin.Multiple solutions for a class of quasilinear elliptic equations involving concave-convex nonlinearities [J].Journal of Mathematics,2013,13(1):6-14.
[6] Filippakis M,Gasinski L,Papageorgiou,N S.On the existence of positive solutions for hemivariational inequalities driven by the p-Laplacian [J].J Glob Optim,2005,31(1):173-189.
[7] Gasinski L.Multiplicity theorems for scalar periodic problems at resonance with p-Laplacian-like operator [J].J Glob Optim,2007,38(3):459-478.
[8] Kristaly A,Marzantowicz W,Varga C.A non-smooth three critical points theorem with applications in differential inclusions [J].J Glob Optim,2010,46(1):49-62.
[9] Teng Kaimin.Multiple solutions for semilinear resonant elliptic problems with discontinuous nonlinearities via nonsmooth double linking theorem [J].J Glob Optim,2010,46(1):89-110.
[10] Amrouss A R El,Kissi F.Multiplicity of solutions for a general p(x)-Laplacian Dirichlet problem [J].Arb Journal of Mathematical Sciences,2013,19(2):205-216.
[11] Shi Xiayang,Ding Xuanhao.Existence and multiplicity of solutions for a general p(x)-Laplacian Neumann problem [J].Nonlinear Analysis,2009,70(10):3715-3720.
[12] Gasinski L,Papageorgiou N S.Multiple solutions for semilinear hemivariational inequalities at resonance [J].Publ Math Debrecen,2001,59(1/2):121-146.
[13] Gasinski L,Papageorgiou N S.A multiplicity result for nonlinear second order periodic equations with nonsmooth potential [J].Bull Belge Math Soc,2002,9(2):245-258.
[14] Harjulehto P,Hästö P,Lê U V,et al.Overview of differential equations with non-standard growth [J].Nonlinear Analysis,2010,72(12):4551-4574.
[15] Clarke F H.Optimization andnonsmooth analysis [M].New York:Wiley,1983.

备注/Memo

备注/Memo:
国家自然科学基金(11271069)
更新日期/Last Update: 1900-01-01