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《Journal of Sichuan Normal University(Natural Science)》 2003-05
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On Existence and Uniqueness of Solutions of a Class of Second Order Semilinear Elliptic Boundary Value Problems

YOU Xiong (Science School, Nanjing Agricultural University, Nanjing 210095, Jiangsu)  
This paper is devoted to the existence and uniqueness of solution of 0boundary value problem of a class of second order semilinear elliptic equations -Δu+f(u)=h. We first present a necessary and sufficient condition for the existence of their classical solutions, and a sufficient condition for the uniqueness of the solutions. Then we give another sufficient condition for the existence and uniqueness of the solutions. These conditions controlling the growth are in integral forms, which differ from those in other literatures. The continuation method used to attack this kind of problems is one of the new points of this article.
【Fund】: 南京农业大学理学院青年创新基金资助项目
【CateGory Index】: O175.25
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【References】
Chinese Journal Full-text Database 3 Hits
1 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
2 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
3 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
【Co-references】
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1 Zhao Ruixing(Meteorological Bureau, Headquarters of the General Staff Chinese People's Liberation Army, Beijing 100081);The Nonlinear Problem of Symmetric Instability and the Periodic Solution of Symmetric Inertia-Gravitational Wave[J];Chinese Journal of Atmospheric Sciences;1994-04
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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 LI Hui,PU Zhi-lin,CHEN Guang-gan(College of Mathematics and Software Science,Sichuan Normal University,Chengdu 610066,Sichuan);The Existence of Solutions for a Class of Nonlinear Elliptic Equations with Critical Exponent[J];Journal of Sichuan Normal University(Natural Science);2006-04
6 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 Li Weiguo; Zhang Danquig(University of Petroleum, Dongying, China 257062);SOLVING OF THE EQUATIONS FOR NEWTONIAN MOTION WITH CONTINUATION METHOD[J];JOURNAL OF THE UNIVERSITY OF PETROLEUM,CHINA;1996-05
9 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
10 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
【Secondary References】
Chinese Journal Full-text Database 4 Hits
1 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
2 LIN Fu-rong,YANG Li-wei(Department of Mathematics,Shantou University,Shantou 515063,Guangdong,China);Existence and Uniqueness of Periodic Solution of a Type of Delay Duffing Equations with a Numerical Solution Method[J];Journal of Shantou University(Natural Science Edition);2008-03
3 LIAO Wei1,2, PU Zhi-lin3(1. College of Mathematics and Information Science,Neijiang Normal College,Neijiang 641112,Sichuan; 2. Key Laboratory of Numerical Simulation of Sichuan Province,Neijiang Normal College,Neijiang 641112,Sichuan;3. College of Mathematics and Software Science,Sichuan Normal University,Chengdu 610066,Sichuan);The Existence of Nontrivial Weak Solution of the Dirichlet Problem for Quasilinear Elliptic Equations[J];Journal of Sichuan Normal University(Natural Science);2009-06
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
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