EXISTENCE OF MULTIPLE SOLUTIONS FOR A QUASILINEAR ELLIPTIC PROBLEM

被引：0

作者：

Cossio, Jorge ^{[1
]}

Herron, Sigifredo ^{[1
]}

Velez, Carlos ^{[1
]}

机构：

[1] Univ Nacl Colombia, Escuela Matemat, Apartado Aereo 3840, Medellin, Colombia

来源：

TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS | 2017年 / 50卷 / 02期

关键词：

Quasilinear elliptic equations; bifurcation theory; multiplicity of solutions; P-LAPLACIAN; BIFURCATION; REGULARITY;

D O I：

10.12775/TMNA.2017.019

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we prove the existence of multiple solutions for a quasilinear elliptic boundary value problem, when the p-derivative at zero and the p-derivative at infinity of the nonlinearity are greater than the first eigenvalue of the p-Laplace operator. Our proof uses bifurcation from infinity and bifurcation from zero to prove the existence of unbounded branches of positive solutions (resp. of negative solutions). We show the existence of multiple solutions and we provide qualitative properties of these solutions.

引用

页码：531 / 551

页数：21

共 23 条

[1] Multiplicity results for some nonlinear elliptic equations [J].

Ambrosetti, A ;

Azorero, JG ;

Peral, I .

JOURNAL OF FUNCTIONAL ANALYSIS, 1996, 137 (01) :219-242

[2] POSITIVE SOLUTIONS OF ASYMPTOTICALLY LINEAR ELLIPTIC EIGENVALUE PROBLEMS [J].

AMBROSETTI, A ;

HESS, P .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1980, 73 (02) :411-422

[3]

[Anonymous], CAMBRIDGE STUDIES AD

[4]

[Anonymous], 1973, Rocky Mountain J. Math., DOI 10.1216/RMJ-1973-3-2-161

[5] Existence of radial solutions for an asymptotically linear p-Laplacian problem [J].

Cossio, Jorge ;

Herron, Sigifredo .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 345 (01) :583-592

[6] Multiple solutions for nonlinear Dirichlet problems via bifurcation and additional results [J].

Cossio, Jorge ;

Herron, Sigifredo ;

Velez, Carlos .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2013, 399 (01) :166-179

[7] Infinitely many radial solutions for a p-Laplacian problem p-superlinear at the origin [J].

Cossio, Jorge ;

Herron, Sigifredo ;

Velez, Carlos .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2011, 376 (02) :741-749

[8]

DEL PEZZO L. M., 2016, ARXIV14124722V2

[9] GLOBAL BIFURCATION FROM THE EIGENVALUES OF THE P-LAPLACIAN [J].

DELPINO, MA ;

MANASEVICH, RF .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1991, 92 (02) :226-251

[10] C1+ALPHA LOCAL REGULARITY OF WEAK SOLUTIONS OF DEGENERATE ELLIPTIC-EQUATIONS [J].

DIBENEDETTO, E .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1983, 7 (08) :827-850

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