Multiple Solutions for a Class of Neumann Elliptic Problems on Compact Riemannian Manifolds with Boundary

被引：6

作者：

Kristaly, Alexandru ^{[1
]}

Papageorgiou, Nikolaos S. ^{[2
]}

Varga, Csaba ^{[3
]}

机构：

[1] Univ Babes Bolyai, Dept Econ, Cluj Napoca 400591, Romania

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

[3] Univ Babes Bolyai, Fac Math & Comp Sci, Cluj Napoca 400084, Romania

来源：

CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES | 2010年 / 53卷 / 04期

关键词：

Riemannian manifold with boundary; Neumann problem; sublinearity at infinity; multiple solutions; MEAN-CURVATURE;

D O I：

10.4153/CMB-2010-073-x

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study a semilinear elliptic problem on a compact Riemannian manifold with boundary, subject to an inhomogeneous Neumann boundary condition. Under various hypotheses on the non-linear terms, depending on their behaviour in the origin and infinity, we prove multiplicity of solutions by using variational arguments.

引用

页码：674 / 683

页数：10

共 8 条

[1]

[Anonymous], 2004, J NONLINEAR CONVEX A

[2]

CARSLAW HS, 1959, CONDUCTION HEAT SOLI, P17

[3]

Diaz J. I., 1985, RES NOTES MATH, V106

[4]

ESCOBAR JF, 1992, J DIFFER GEOM, V35, P21

[5] CONFORMAL DEFORMATION OF A RIEMANNIAN METRIC TO A SCALAR FLAT METRIC WITH CONSTANT MEAN-CURVATURE ON THE BOUNDARY [J].

ESCOBAR, JF .

ANNALS OF MATHEMATICS, 1992, 136 (01) :1-50

[6] Conformal metrics with prescribed mean curvature on the boundary [J].

Escobar, JF .

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 1996, 4 (06) :559-592

[7] EXISTENCE OF A POSITIVE SOLUTION OF A GENERAL QUASI-LINEAR ELLIPTIC EQUATION WITH A NONLINEAR BOUNDARY-CONDITION OF MIXED TYPE [J].

MICHALEK, R .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1990, 15 (09) :871-882

[8] A three critical points theorem revisited [J].

Ricceri, Biagio .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2009, 70 (09) :3084-3089

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