EXISTENCE OF POSITIVE SOLUTION TO-Δu=f(x,u) WHEN f CHANGES SIGNS

数学物理学报(英文版) ›› 1994, Vol. 14 ›› Issue (S1): 40-45.

EXISTENCE OF POSITIVE SOLUTION TO-Δu=f(x,u) WHEN f CHANGES SIGNS

姜明

Dept. Appl. Math, Beijing Institute of Technology, Beijing 100081, China

收稿日期:1992-03-06 出版日期:1994-12-31 发布日期:1994-12-31
基金资助:
Research supported by a Youth Grant from National Natural Science Foundation of China.

EXISTENCE OF POSITIVE SOLUTION TO-Δu=f(x,u) WHEN f CHANGES SIGNS

Jiang Ming

Dept. Appl. Math, Beijing Institute of Technology, Beijing 100081, China

Received:1992-03-06 Online:1994-12-31 Published:1994-12-31
Supported by:
Research supported by a Youth Grant from National Natural Science Foundation of China.

摘要/Abstract

摘要： The existence of positive solutions to the semlinear elliptic boundary value problem
-Δ=f(x,u) in Ω and u=0 on ∂Ω is studied in this paper. The result obtained differs from the other known results in that the positivity of the solution does not follow from the positivity of f.Our result roughly says that if Ω is not too wide in some one direction, there is always a positive solution even if f changes signs, which is proved using the so-calles sub-super solution approach.

关键词: Positive solution, Semliinear elliptic boundary valed problem

Abstract: The existence of positive solutions to the semlinear elliptic boundary value problem
-Δ=f(x,u) in Ω and u=0 on ∂Ω is studied in this paper. The result obtained differs from the other known results in that the positivity of the solution does not follow from the positivity of f.Our result roughly says that if Ω is not too wide in some one direction, there is always a positive solution even if f changes signs, which is proved using the so-calles sub-super solution approach.

Key words: Positive solution, Semliinear elliptic boundary valed problem

姜明. EXISTENCE OF POSITIVE SOLUTION TO-Δu=f(x,u) WHEN f CHANGES SIGNS[J]. 数学物理学报(英文版), 1994, 14(S1): 40-45.

Jiang Ming. EXISTENCE OF POSITIVE SOLUTION TO-Δu=f(x,u) WHEN f CHANGES SIGNS[J]. Acta mathematica scientia,Series B, 1994, 14(S1): 40-45.

[1]	张肖, 吉国兴. SOLUTIONS TO THE SYSTEM OF OPERATOR EQUATIONS AXB=C=BXA[J]. 数学物理学报(英文版), 2018, 38(4): 1143-1150.
[2]	王朋燕, 王永忠. POSITIVE SOLUTIONS FOR A WEIGHTED FRACTIONAL SYSTEM[J]. 数学物理学报(英文版), 2018, 38(3): 935-949.
[3]	廖家锋, 蒲洋, 唐春雷. MULTIPLICITY OF POSITIVE SOLUTIONS FOR A CLASS OF CONCAVE-CONVEX ELLIPTIC EQUATIONS WITH CRITICAL GROWTH[J]. 数学物理学报(英文版), 2018, 38(2): 497-518.
[4]	贾慧芳, 李工宝. MULTIPLICITY AND CONCENTRATION BEHAVIOUR OF POSITIVE SOLUTIONS FOR SCHRÖDINGER-KIRCHHOFF TYPE EQUATIONS INVOLVING THE p-LAPLACIAN IN R^N[J]. 数学物理学报(英文版), 2018, 38(2): 391-418.
[5]	马如云, 高红亮. MULTIPLE POSITIVE SOLUTIONS FOR A CLASS OF SEMIPOSITONE NEUMANN PROBLEMS WITH SINGULAR φ-LAPLACIAN[J]. 数学物理学报(英文版), 2017, 37(5): 1472-1482.
[6]	Yan LI. NONEXISTENCE OF POSITIVE SOLUTIONS FOR A SEMI-LINEAR EQUATION INVOLVING THE FRACTIONAL LAPLACIAN IN R^N[J]. 数学物理学报(英文版), 2016, 36(3): 666-682.
[7]	韦忠礼. SOME NECESSARY AND SUFFICIENT CONDITIONS FOR EXISTENCE OF POSITIVE SOLUTIONS FOR THIRD ORDER SINGULAR SUBLINEAR MULTI-POINT BOUNDARY VALUE PROBLEMS[J]. 数学物理学报(英文版), 2014, 34(6): 1795-1810.
[8]	Zagharide Zine EL ABIDINE. COMBINED EFFECTS IN A SEMILINEAR POLYHARMONIC PROBLEM IN THE UNIT BALL[J]. 数学物理学报(英文版), 2014, 34(5): 1404-1416.
[9]	范海宁, 刘晓春. MULTIPLE POSITIVE SOLUTIONS FOR A CLASS OF QUASI-LINEAR ELLIPTIC EQUATIONS INVOLVING CRITICAL SOBOLEV EXPONENT[J]. 数学物理学报(英文版), 2014, 34(4): 1111-1126.
[10]	Tsing-San HSU. MULTIPLE POSITIVE SOLUTIONS FOR QUASILINEAR ELLIPTIC PROBLEMS INVOLVING CONCAVE-CONVEX NONLINEARITIES AND MULTIPLE HARDY-TYPE TERMS[J]. 数学物理学报(英文版), 2013, 33(5): 1314-1328.
[11]	李工宝, 叶红雨. EXISTENCE OF POSITIVE SOLUTIONS TO SEMILINEAR ELLIPTIC SYSTEMS IN RN WITH ZERO MASS[J]. 数学物理学报(英文版), 2013, 33(4): 913-928.
[12]	李楠, 王长有. NEW EXISTENCE RESULTS OF POSITIVE SOLUTION FOR A CLASS OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS[J]. 数学物理学报(英文版), 2013, 33(3): 847-854.
[13]	李圆晓, 高文杰. EXISTENCE OF MULTIPLE SOLUTIONS FOR SINGULAR QUASILINEAR ELLIPTIC SYSTEM WITH CRITICAL SOBOLEV-HARDY EXPONENTS AND CONCAVE-CONVEX TERMS[J]. 数学物理学报(英文版), 2013, 33(1): 107-121.
[14]	Sma?l Djebali, Ouiza Sa?fi, 闫宝强. POSITIVE SOLUTIONS FOR SINGULAR BVPs ON THE POSITIVE HALF-LINE ARISING FROM EPIDEMIOLOGY AND COMBUSTION THEORY[J]. 数学物理学报(英文版), 2012, 32(2): 672-694.
[15]	赵增勤. NONEXISTENCE AND EXISTENCE OF POSITIVE SOLUTIONS FOR 2nTH-ORDER SINGULAR SUPERLINEAR PROBLEMS WITH#br# STRUM-LIOUVILLE BOUNDARY CONDITIONS[J]. 数学物理学报(英文版), 2011, 31(4): 1569-1582.

EXISTENCE OF POSITIVE SOLUTION TO-Δu=f(x,u) WHEN f CHANGES SIGNS

EXISTENCE OF POSITIVE SOLUTION TO-Δu=f(x,u) WHEN f CHANGES SIGNS

PDF (PC)

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

Metrics

本文评价

推荐阅读 10