Positive Solutions for Nonlinear Nonhomogeneous Robin Problems

被引：8

作者：

Gasinski, Leszek ^{[1
]}

O'Regan, Donal ^{[2
]}

Papageorgiou, Nikolaos S. ^{[3
]}

机构：

[1] Jagiellonian Univ, Fac Math & Comp Sci, PL-30348 Krakow, Poland

[2] Natl Univ Ireland, Sch Math Stat & Appl Math, Galway, Ireland

[3] Natl Tech Univ Athens, Dept Math, Athens 15780, Greece

来源：

ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN | 2015年 / 34卷 / 04期

关键词：

Positive solution; nonlinear regularity; nonlinear maximum principle; logistic equations; smallest positive solution; ELLIPTIC EIGENVALUE PROBLEMS; MULTIPLICITY THEOREMS; EXISTENCE; SIGN;

D O I：

10.4171/ZAA/1548

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider a nonlinear, nonhomogeneous Robin problem with a Caratheodory reaction which satisfies certain general growth conditions near 0(+) and near +infinity. We show the existence and regularity of positive solutions, the existence of a smallest positive solution and under an additional condition on the reaction, we show the uniqueness of the positive solutions. We then show that our setting incorporates certain parametric Robin equations of interest such as nonlinear equidiffusive logistic equations.

引用

页码：435 / 458

页数：24

共 26 条

[1] Allegretto W, 1998, NONLINEAR ANAL-THEOR, V32, P819
[2] [Anonymous], Pure and Applied Mathematics, VVII
[3] Autuori G, 2013, ADV DIFFERENTIAL EQU, V18, P1
[4] Buttazzo G, 1998, Oxford Lecture Series in Mathematics and its Applications
[5] Multiple solutions for an eigenvalue problem involving p-Laplacian type operators
Colasuonno, Francesca
Pucci, Patrizia
Varga, Csaba
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2012, 75 (12) : 4496 - 4512
[6] DIAZ JI, 1987, CR ACAD SCI I-MATH, V305, P521
[7] Existence and non-existence results for quasilinear elliptic exterior problems with nonlinear boundary conditions
Filippucci, Roberta
Pucci, Patrizia
Radulescu, Vicentiu
[J]. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2008, 33 (04) : 706 - 717
[8] On nonlinear elliptic hemivariational inequalities of second order
Gasinski, L
Papageorgiou, LS
[J]. ACTA MATHEMATICA SCIENTIA, 2004, 24 (03) : 451 - 462
[9] Gasinski L, 2006, Nonlinear analysis
[10] Gasinski L., 2010, HDB NONCONVEX ANAL A, p183

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