EXISTENCE OF THE MINIMAL POSITIVE SOLUTION OF SOME NONLINEAR ELLIPTIC SYSTEMS WHEN THE NONLINEARITY IS THE SUM OF A SUBLINEAR AND A SUPERLINEAR TERM

Applied Mathematics and Mechanics (English Edition) ›› 2000, Vol. 21 ›› Issue (3): 283-290.

EXISTENCE OF THE MINIMAL POSITIVE SOLUTION OF SOME NONLINEAR ELLIPTIC SYSTEMS WHEN THE NONLINEARITY IS THE SUM OF A SUBLINEAR AND A SUPERLINEAR TERM

Nicolae Tarfulea

Department of Mathematics, the Pennsylvania State University, University Park, PA 16802, USA

收稿日期:1999-03-01 出版日期:2000-03-18 发布日期:2000-03-18
通讯作者: Chien Weizang

EXISTENCE OF THE MINIMAL POSITIVE SOLUTION OF SOME NONLINEAR ELLIPTIC SYSTEMS WHEN THE NONLINEARITY IS THE SUM OF A SUBLINEAR AND A SUPERLINEAR TERM

Nicolae Tarfulea

Department of Mathematics, the Pennsylvania State University, University Park, PA 16802, USA

Received:1999-03-01 Online:2000-03-18 Published:2000-03-18

摘要/Abstract

摘要： It is shown that there exists Λ>0 such that, for every λ∈(0,Λ), the semilinear elliptic system:-Δu=λu｜u｜^q-1+u｜u｜ ^p-1-v in Ω,- Δv=δu-γv in Ω, u=v=0 on ∂Ω, where Ω∈R^N(N≥2) is a bounded domain with smooth boundary and 0<q<1<p,has a minimal positive solution (uλ,vλ). Moreover: uλ and vλ are strictly increasing with respect to λ.

关键词: reaction diffusion system, positive solution, nonlinear equation

Abstract: It is shown that there exists Λ>0 such that, for every λ∈(0,Λ), the semilinear elliptic system:-Δu=λu｜u｜^q-1+u｜u｜ ^p-1-v in Ω,- Δv=δu-γv in Ω, u=v=0 on ∂Ω, where Ω∈R^N(N≥2) is a bounded domain with smooth boundary and 0<q<1<p,has a minimal positive solution (uλ,vλ). Moreover: uλ and vλ are strictly increasing with respect to λ.

Key words: reaction diffusion system, positive solution, nonlinear equation

中图分类号:

O175.25

Nicolae Tarfulea . EXISTENCE OF THE MINIMAL POSITIVE SOLUTION OF SOME NONLINEAR ELLIPTIC SYSTEMS WHEN THE NONLINEARITY IS THE SUM OF A SUBLINEAR AND A SUPERLINEAR TERM[J]. Applied Mathematics and Mechanics (English Edition), 2000, 21(3): 283-290.

[1]	Yanhai LIN, Liancun ZHENG, Lianxi MA. Heat transfer characteristics of thin power-law liquid films over horizontal stretching sheet with internal heating and variable thermal coefficient[J]. Applied Mathematics and Mechanics (English Edition), 2016, 37(12): 1587-1596.
[2]	袁益让;李长峰;孙同军;刘允欣. Characteristic fractional step finite difference method for nonlinear section coupled system[J]. Applied Mathematics and Mechanics (English Edition), 2014, 35(10): 1311-1330.
[3]	纪玉德郭彦平禹长龙. Positive solutions to (n-1,1) m-point boundary value problems with dependence on the first order derivative[J]. Applied Mathematics and Mechanics (English Edition), 2009, 30(4): 527-536.
[4]	刘冠琦王玉文史峻平. Existence and nonexistence of positive solutions of semilinear elliptic equation with inhomogeneous strong Allee effect[J]. Applied Mathematics and Mechanics (English Edition), 2009, 30(11): 1461-1468.
[5]	洪梅张韧薛峰刘科峰. Space-time objective decomposition of vortex equations and mechanism analysis of subtropical high abnormal activities[J]. Applied Mathematics and Mechanics (English Edition), 2009, 30(10): 1263-1270.
[6]	莫嘉琪;王辉. SHIFT OF SHOCK POSITION FOR A CLASS OF NONLINEAR SINGULARLY PERTURBED PROBLEMS[J]. Applied Mathematics and Mechanics (English Edition), 2005, 26(1): 58-62 .
[7]	张正策;李开泰. STRUCTURE OF NONNEGATIVE NONTRIVIAL AND POSITIVE SOLUTIONS OF SINGULARLY PERTURBED p-LAPLACE EQUATIONS[J]. Applied Mathematics and Mechanics (English Edition), 2004, 25(8): 929-936.
[8]	曲文波;张中新;武俊德. POSITIVE SOLUTIONS TO A SINGULAR SECOND ORDER THREE-POINT BOUNDARY VALUE PROBLEM[J]. Applied Mathematics and Mechanics (English Edition), 2002, 23(7): 854-866.
[9]	何吉欢. A NOTE ON DELTA-PERTURBATION EXPANSION METHOD[J]. Applied Mathematics and Mechanics (English Edition), 2002, 23(6): 634-638.
[10]	姚庆六. THE POSITIVE SOLUTION OF CLASSICAL GELFAND MODEL WITH COEFFICIENT THAT CHANGE SIGN[J]. Applied Mathematics and Mechanics (English Edition), 2002, 23(12): 1458-1463.
[11]	李仁贵;刘立山. POSITIVE SOLUTIONS OF BOUNDARY VALUE PROBLEMS FOR SECOND-ORDER SINGULAR NONLINEAR DIFFERENTIAL EQUATIONS[J]. Applied Mathematics and Mechanics (English Edition), 2001, 22(4): 495-500.
[12]	白占兵. EXISTENCE AND MULTIPLICITY OF POSITIVE SOLUTIONS FOR A FOURTH-ORDER P-LAPLACE EQUATIONS[J]. Applied Mathematics and Mechanics (English Edition), 2001, 22(12): 1476-1480.
[13]	吴新元. A SIGNIFICANT IMPROVEMENT ON NEWTON’S ITERATIVE METHOD[J]. Applied Mathematics and Mechanics (English Edition), 1999, 20(8): 924-927.
[14]	常海萍;黄太平. THE AUTO-ADJUSTABLE DAMPING METHOD FOR SOLVING NONLINEAR EQUATIONS[J]. Applied Mathematics and Mechanics (English Edition), 1998, 19(2): 163-168.
[15]	董卫. UNIQUENESS OF SOLUTIONS FOR A CLASS OF NON-LINEAR VOLTERRA INTEGRAL EQUATIONS WITHOUT CONTINUITY[J]. Applied Mathematics and Mechanics (English Edition), 1997, 18(12): 1191-1196.

EXISTENCE OF THE MINIMAL POSITIVE SOLUTION OF SOME NONLINEAR ELLIPTIC SYSTEMS WHEN THE NONLINEARITY IS THE SUM OF A SUBLINEAR AND A SUPERLINEAR TERM

EXISTENCE OF THE MINIMAL POSITIVE SOLUTION OF SOME NONLINEAR ELLIPTIC SYSTEMS WHEN THE NONLINEARITY IS THE SUM OF A SUBLINEAR AND A SUPERLINEAR TERM

PDF

可视化

被引次数

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

编辑推荐

Metrics

本文评价