Existence and multiplicity results for a class of semilinear elliptic equations

被引：5
作者：
Bobkov, Vladimir [1 ,2 ]
Drabek, Pavel [1 ,2 ]
Hernandez, Jesus [3 ]
机构：
[1] Univ West Bohemia, Fac Sci Appl, Dept Math, Univ 8, Plzen 30100, Czech Republic
[2] Univ West Bohemia, Fac Sci Appl, NTIS, Univ 8, Plzen 30100, Czech Republic
[3] Fac Matemat, Inst Matemat Interdisciplinar, Madrid 28040, Spain
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2020年 / 200卷
关键词：
Existence; Multiplicity; Branches; Positive solutions; Non-Lipschitz nonlinearities; Variational methods; Flat solutions; Compact support solutions; FRACTIONAL ORDER AUTOCATALYSIS; TRAVELING-WAVES; LOCAL SUPERLINEARITY; POSITIVE SOLUTIONS; BIFURCATION; NONLINEARITIES; INDEFINITE; EVOLUTION; BOUNDARY; CONCAVE;
D O I：
10.1016/j.na.2020.112017
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study the existence and multiplicity of nonnegative solutions, as well as the behavior of corresponding parameter-dependent branches, to the equation -Delta u = (1 - u)u(m) - lambda u(n) in a bounded domain Omega subset of R-N endowed with the zero Dirichlet boundary data, where 0 < m <= 1 and n > 0. When lambda > 0, the obtained solutions can be seen as steady states of the corresponding reaction-diffusion equation describing a model of isothermal autocatalytic chemical reaction with termination. In addition to the main new results, we formulate a few relevant conjectures. (C) 2020 Elsevier Ltd. All rights reserved.
引用
收藏
页数：25
相关论文
共 35 条
[1]   ESTIMATES NEAR THE BOUNDARY FOR SOLUTIONS OF ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS SATISFYING GENERAL BOUNDARY CONDITIONS .1. [J].
AGMON, S ;
DOUGLIS, A ;
NIRENBERG, L .
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1959, 12 (04) :623-727
[2]   Elliptic problems with nonlinearities indefinite in sign [J].
Alama, S ;
Tarantello, G .
JOURNAL OF FUNCTIONAL ANALYSIS, 1996, 141 (01) :159-215
[3]   COMBINED EFFECTS OF CONCAVE AND CONVEX NONLINEARITIES IN SOME ELLIPTIC PROBLEMS [J].
AMBROSETTI, A ;
BREZIS, H ;
CERAMI, G .
JOURNAL OF FUNCTIONAL ANALYSIS, 1994, 122 (02) :519-543
[4]   S-shaped bifurcation branch in a quasilinear multivalued model arising in climatology [J].
Arcoya, D ;
Diaz, JI ;
Tello, L .
JOURNAL OF DIFFERENTIAL EQUATIONS, 1998, 150 (01) :215-225
[5]   REMARKS ON SUBLINEAR ELLIPTIC-EQUATIONS [J].
BREZIS, H ;
OSWALD, L .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1986, 10 (01) :55-64
[6]   S-SHAPED BIFURCATION CURVES [J].
BROWN, KJ ;
IBRAHIM, MMA ;
SHIVAJI, R .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1981, 5 (05) :475-486
[7]   Symmetry in an elliptic problem and the blow-up set of a quasilinear heat equation. [J].
Cortazar, C ;
Elgueta, M ;
Felmer, P .
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1996, 21 (3-4) :507-520
[8]  
CRANDALL MG, 1973, ARCH RATION MECH AN, V52, P161, DOI 10.1007/BF00282325
[9]  
de Figueiredo DG, 2006, J EUR MATH SOC, V8, P269
[10]   Local superlinearity and sublinearity for indefinite semilinear elliptic problems [J].
De Figueiredo, DG ;
Gossez, JP ;
Ubilla, P .
JOURNAL OF FUNCTIONAL ANALYSIS, 2003, 199 (02) :452-467
1234