A nonresonance condition for radial solutions of a nonlinear Neumann elliptic problem

被引：1

作者：

Sfecci, Andrea ^{[1
]}

机构：

[1] SISSA Int Sch Adv Studies, I-34136 Trieste, Italy

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2012年 / 75卷 / 16期

关键词：

Neumann problem; Radial solutions; Nonresonance; Time-map; PERIODIC-SOLUTIONS; EXISTENCE; EQUATIONS;

D O I：

10.1016/j.na.2012.06.023

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove an existence result for radial solutions of a Neumann elliptic problem whose nonlinearity asymptotically lies between the first two eigenvalues. To this aim, we introduce an alternative nonresonance condition with respect to the second eigenvalue which, in the scalar case, generalizes the classical one, in the spirit of Fonda et al. (1991) [2]. Our approach also applies for nonlinearities which do not necessarily satisfy a subcritical growth assumption. (C) 2012 Elsevier Ltd. All rights reserved.

引用

收藏

页码：6191 / 6202

页数：12

相关论文

共 21 条

[1] On a p-Laplace Neumann problem with asymptotically asymmetric perturbations [J].

Alif, M ;

Omari, P .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2002, 51 (03) :369-389

[2]

[Anonymous], Handbook of Mathematical Functions

[3]

[Anonymous], 2003, INT J PHYTOREMEDIATI, DOI DOI 10.1080/0003681031000154918

[4] Radial solutions for Neumann problems involving mean curvature operators in Euclidean and Minkowski spaces [J].

Bereanu, Cristian ;

Jebelean, Petru ;

Mawhin, Jean .

MATHEMATISCHE NACHRICHTEN, 2010, 283 (03) :379-391

[5] ON PERIODIC-SOLUTIONS OF SUBLINEAR DUFFING EQUATIONS [J].

DING, TG ;

IANNACCI, R ;

ZANOLIN, F .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1991, 158 (02) :316-332

[6] EXISTENCE AND MULTIPLICITY RESULTS FOR PERIODIC-SOLUTIONS OF SEMILINEAR DUFFING EQUATIONS [J].

DING, TR ;

IANNACCI, R ;

ZANOLIN, F .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1993, 105 (02) :364-409

[7] PERIODIC-SOLUTIONS OF A 2ND-ORDER DIFFERENTIAL-EQUATION WITH ONE-SIDED GROWTH RESTRICTIONS ON THE RESTORING TERM [J].

FERNANDES, L ;

ZANOLIN, F .

ARCHIV DER MATHEMATIK, 1988, 51 (02) :151-163

[8]

Fernandes M.L.C., 1989, DIFFERENTIAL INTEGRA, V2, P63

[9] ON THE EXISTENCE OF PERIODIC-SOLUTIONS FOR SCALAR 2ND-ORDER DIFFERENTIAL-EQUATIONS WHEN ONLY THE ASYMPTOTIC-BEHAVIOR OF THE POTENTIAL IS KNOWN [J].

FONDA, A .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1993, 119 (02) :439-445

[10] ON THE USE OF TIME-MAPS FOR THE SOLVABILITY OF NONLINEAR BOUNDARY-VALUE-PROBLEMS [J].

FONDA, A ;

ZANOLIN, F .

ARCHIV DER MATHEMATIK, 1992, 59 (03) :245-259