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《Journal of Sichuan Normal University(Natural Science)》 2006-04
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The Existence of Solutions for a Class of Nonlinear Elliptic Equations with Critical Exponent

LI Hui,PU Zhi-lin,CHEN Guang-gan(College of Mathematics and Software Science,Sichuan Normal University,Chengdu 610066,Sichuan)  
In this paper,a class of elliptic equations with critical exponent is studied.By applying the concentration-compactness principle and the Mountain Pass Lemma,the existence of the nontrivial solutions is proved in a bounded domain ΩR~N.
【Fund】: 国家自然科学基金预研基金;; 四川省教育厅自然科学重点基金资助项目
【CateGory Index】: O175.25
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【References】
Chinese Journal Full-text Database 4 Hits
1 HUANG Juan,PU Zhi-lin,CHEN Guang-gan(College of Mathematics and Software Science,Sichuan Normal University,Chengdu 610066,Sichuan);The Concentration-compactness of a Nonlinear Elliptic Equation on R~N[J];Journal of Sichuan Normal University(Natural Science);2006-06
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3 HUANG Juan,PU Zhi-lin,CHEN Guang-gan(College of Mathematics and Software Science,Sichuan Normal University,Chengdu 610066,Sichuan);The Properties of the Nehari Manifold for the Nonlinear Elliptic Equation Involving a Sublinear Term[J];Journal of Sichuan Normal University(Natural Science);2008-02
4 ZHANG Yan1,PU Zhi-lin2,CHEN Bo-tao31.School of Mathematics and Computer Science,Xihua University,Chengdu 610039,China;2.School of Mathematics and Software,Sichuan Normal University,Chengdu 610066,China;3.Department of Mathematics,Changjiang Teacher's College,Chongqing 408000,Chin;Boundedness of the Solution to the Nonlinear Kirchhoff Equation[J];Journal of Southwest China Normal University(Natural Science Edition);2008-06
【Citations】
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1 CHEN Shun-qing (Department of Mathematics, Daxian Teacher's College, Dazhou 635000, Sichuan);The Existence of Positive Solutions for a Class Singular Initial Value Problems[J];Journal of Sichuan Normal University(Natural Science);2004-02
2 LIAO Wei,PU Zhi-lin(College of Mathematics and Software Science,Sichuan Normal University,Chengdu 610066,Sichuan);The Existence of Nontrivial Weak Solutions of a Class of p-Laplacian Equationt without Compactness[J];Journal of Sichuan Normal University(Natural Science);2006-01
3 RAO Ruo-fengDept. of Science, Jiujiang College, Jiujiang Jiangxi 332005, China;Notes on A Class of Semi-Linear Elliptic Equations with the First Eigenvalue, Involving the Critical Sobolev Exponents[J];Journal of Southwest China Normal University(Natural Science);2004-04
4 SONG Shu-zhi, TANG Chun-leiSchool of Mathematics and Finance, Southwest China Normal University, Chongqing 400715, China;Existence Theorem for Quasilinear Elliptic Resonance Problems[J];Journal of Southwest China Normal University(Natural Science);2005-01
【Co-citations】
Chinese Journal Full-text Database 9 Hits
1 HUANG Juan,PU Zhi-lin,CHEN Guang-gan(College of Mathematics and Software Science,Sichuan Normal University,Chengdu 610066,Sichuan);The Concentration-compactness of a Nonlinear Elliptic Equation on R~N[J];Journal of Sichuan Normal University(Natural Science);2006-06
2 ZHAO Zhi-kun~(1,2),PU Zhi-lin~2(1.Department of Mathematics and Information Science,Mianyang Normal University,Mianyang 621000,Sichuan;2.College of Mathematics and Software Science,Sichuan Normal University, Chengdu 610066,Sichuan);The Existence of Solutions for a Class of Elliptic Equations with Indefinite Weight[J];Journal of Sichuan Normal University(Natural Science);2006-06
3 HUANG Juan,PU Zhi-lin,CHEN Guang-gan(College of Mathematics and Software Science,Sichuan Normal University,Chengdu 610066,Sichuan);The Properties of the Nehari Manifold for the Nonlinear Elliptic Equation Involving a Sublinear Term[J];Journal of Sichuan Normal University(Natural Science);2008-02
4 HUANG Xin1,PU Zhi-lin1,LUO Tian-qi2(1.College of Mathematics and Software Science,Sichuan Normal University,Chengdu 610066,Sichuan;2.Department of Mathematics,Leshan Teacher's College,Leshan 614004,Sichuan);Application of the Mountain Pass Theorem to Asymptotically Linear Elliptic Equations[J];Journal of Sichuan Normal University(Natural Science);2008-02
5 WANG Xiao-jing,PU Zhi-lin,DAI Bing(College of Mathematics and Software Science,Sichuan Normal University,Chengdu 610066,Sichuan);The Solutions for a Superlinear Elliptic Equation on R~N[J];Journal of Sichuan Normal University(Natural Science);2010-02
6 KE Xiao-feng,TANG Chun-leiSchool of Mathematics and Statistics,Southwest University,Chongqing 400715, Chin;Existence of Solution for p-Laplacian Equations at Resonance[J];Journal of Southwest University(Natural Science Edition);2008-06
7 DING Ling1,2, TANG Chun-lei11.School of Mathematics and Statistics,Southwest University,Chongqing 400715,China;2.Department of Mathematics,Xiangfan University,Xiangfan Hubei 441053,Chin;Multiple Positive Solutions for Semilinear Elliptic Equations Involving Hardy Terms and Hardy-Sobolev Critical Exponents[J];Journal of Southwest University(Natural Science Edition);2008-06
8 HUANGLi,WU Xing-ping,TANG Chun-lei School of Mathematics and Statistics,Southwest University,Chongqing 400715,China;Existence and Multiplicity of Solutions for p-Laplacian Equations with Weighted Hardy-Sobolev Critical Exponents[J];Journal of Southwest University(Natural Science Edition);2009-02
9 YAN Dong-mingCollege of Mathematics and Information Science,Northwest Normal University,Lanzhou Gansu 730070,China;The Existence for a Class of Fourth-Order Two-Point Boundary Value Problem[J];Journal of Southwest University(Natural Science Edition);2009-09
【Co-references】
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1 DENG Lihu1,2,MU Chunlai1 (1.Mathematical College,Sichuan University,Chengdu 610064 China; 2.Department of Applied Mathematics,Dongguan Institute of Technology,Guangdong Dongguan 523106,China);Multiple Solution of a Class of Quasilinear Elliptic Equation[J];Journal of Sichuan University (Natural Science Edition);2003-05
2 YOU Xiong (Science School, Nanjing Agricultural University, Nanjing 210095, Jiangsu);On Existence and Uniqueness of Solutions of a Class of Second Order Semilinear Elliptic Boundary Value Problems[J];Journal of Sichuan Normal University(Natural Science);2003-05
3 CHEN Shun-qing (Department of Mathematics, Daxian Teacher's College, Dazhou 635000, Sichuan);The Existence of Positive Solutions for a Class Singular Initial Value Problems[J];Journal of Sichuan Normal University(Natural Science);2004-02
4 LIAO Wei,PU Zhi-lin(College of Mathematics and Software Science,Sichuan Normal University,Chengdu 610066,Sichuan);The Existence of Nontrivial Weak Solutions of a Class of p-Laplacian Equationt without Compactness[J];Journal of Sichuan Normal University(Natural Science);2006-01
5 LIAO Wei1, PU Zhi-lin2(1. Department of Mathematics, Neijiang Teacher’s College, Neijiang 641112, Sichuan; 2. College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066, Sichuan);The Existence of Positive Solution of the Dirichlet Problem for Some Quasilinear Elliptic Equations[J];Journal of Sichuan Normal University(Natural Science);2007-01
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8 RAO Ruofeng Department of Mathematics, Zhaoqing College, Zhaoqing 526061, Guangdong, China.;EXISTENCE OF MULTIPLE NONTRIVIAL SOLUTIONS FOR THE CRITICAL ELLIPTIC EQUATION -△_u=λ_k~u+|u|~(2~*-2_u)+f(x,u)[J];Chinese Annals of Mathematics,series A;2005-06
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【Secondary Citations】
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1 CHEN Guang-gan, PU Zhi-lin, LU Hong (College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066, Sichuan);The Robust Convergence of the ODE System[J];Journal of Sichuan Normal University(Natural Science);2002-01
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3 Da Qing JIANG(Department of Mathematics, Northeast Normal University, Changchun 130024, P. R. China)(E-mail: daqingjiang@163.com);Positive Solutions to Singular Semilinear and Superlinear Boundary Value Problems for the One-Dimensional p-Laplacian[J];Acta Mathematica Sinica;2002-04
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