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

Acta mathematica scientia,Series B ›› 1994, Vol. 14 ›› Issue (S1): 40-45.

• Articles • Previous Articles Next Articles

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.

Abstract

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

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.

Trendmd

[1]	Xiao ZHANG, Guoxing JI. SOLUTIONS TO THE SYSTEM OF OPERATOR EQUATIONS AXB=C=BXA [J]. Acta mathematica scientia,Series B, 2018, 38(4): 1143-1150.
[2]	Pengyan WANG, Yongzhong WANG. POSITIVE SOLUTIONS FOR A WEIGHTED FRACTIONAL SYSTEM [J]. Acta mathematica scientia,Series B, 2018, 38(3): 935-949.
[3]	Jiafeng LIAO, Yang PU, Chunlei TANG. MULTIPLICITY OF POSITIVE SOLUTIONS FOR A CLASS OF CONCAVE-CONVEX ELLIPTIC EQUATIONS WITH CRITICAL GROWTH [J]. Acta mathematica scientia,Series B, 2018, 38(2): 497-518.
[4]	Huifang JIA, Gongbao LI. MULTIPLICITY AND CONCENTRATION BEHAVIOUR OF POSITIVE SOLUTIONS FOR SCHRÖDINGER-KIRCHHOFF TYPE EQUATIONS INVOLVING THE p-LAPLACIAN IN R^N [J]. Acta mathematica scientia,Series B, 2018, 38(2): 391-418.
[5]	Ruyun MA, Hongliang GAO. MULTIPLE POSITIVE SOLUTIONS FOR A CLASS OF SEMIPOSITONE NEUMANN PROBLEMS WITH SINGULAR φ-LAPLACIAN [J]. Acta mathematica scientia,Series B, 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]. Acta mathematica scientia,Series B, 2016, 36(3): 666-682.
[7]	WEI Zhong-Li. SOME NECESSARY AND SUFFICIENT CONDITIONS FOR EXISTENCE OF POSITIVE SOLUTIONS FOR THIRD ORDER SINGULAR SUBLINEAR MULTI-POINT BOUNDARY VALUE PROBLEMS [J]. Acta mathematica scientia,Series B, 2014, 34(6): 1795-1810.
[8]	Zagharide Zine EL ABIDINE. COMBINED EFFECTS IN A SEMILINEAR POLYHARMONIC PROBLEM IN THE UNIT BALL [J]. Acta mathematica scientia,Series B, 2014, 34(5): 1404-1416.
[9]	FAN Hai-Ning, LIU Xiao-Chun. MULTIPLE POSITIVE SOLUTIONS FOR A CLASS OF QUASI-LINEAR ELLIPTIC EQUATIONS INVOLVING CRITICAL SOBOLEV EXPONENT [J]. Acta mathematica scientia,Series B, 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]. Acta mathematica scientia,Series B, 2013, 33(5): 1314-1328.
[11]	LI Gong-Bao, YE Hong-Yu. EXISTENCE OF POSITIVE SOLUTIONS TO SEMILINEAR ELLIPTIC SYSTEMS IN RN WITH ZERO MASS [J]. Acta mathematica scientia,Series B, 2013, 33(4): 913-928.
[12]	LI Nan, WANG Chang-You. NEW EXISTENCE RESULTS OF POSITIVE SOLUTION FOR A CLASS OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS [J]. Acta mathematica scientia,Series B, 2013, 33(3): 847-854.
[13]	LI Yuan-Xiao, GAO Wen-Jie. EXISTENCE OF MULTIPLE SOLUTIONS FOR SINGULAR QUASILINEAR ELLIPTIC SYSTEM WITH CRITICAL SOBOLEV-HARDY EXPONENTS AND CONCAVE-CONVEX TERMS [J]. Acta mathematica scientia,Series B, 2013, 33(1): 107-121.
[14]	Sma?l Djebali, Ouiza Sa?fi, YAN Bao-Qiang. POSITIVE SOLUTIONS FOR SINGULAR BVPs ON THE POSITIVE HALF-LINE ARISING FROM EPIDEMIOLOGY AND COMBUSTION THEORY [J]. Acta mathematica scientia,Series B, 2012, 32(2): 672-694.
[15]	ZHAO Zeng-Qin. NONEXISTENCE AND EXISTENCE OF POSITIVE SOLUTIONS FOR 2nTH-ORDER SINGULAR SUPERLINEAR PROBLEMS WITH#br# STRUM-LIOUVILLE BOUNDARY CONDITIONS [J]. Acta mathematica scientia,Series B, 2011, 31(4): 1569-1582.

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

PDF (PC)

Abstract

Cite this article

share this article

References

Related Articles 15

Metrics

Comments

Recommended 10