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Zbl 1237.35043
Rădulescu, Vicenţiu; Repovš, Dušan
Combined effects in nonlinear problems arising in the study of anisotropic continuous media. (English)
[J] Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 75, No. 3, 1524-1530 (2012). ISSN 0362-546X

This paper deals with the qualitative analysis of positive solutions for a class of nonlinear elliptic equations with Dirichlet boundary condition. The main features are the following: (i) the presence of variable potential functions; (ii) the study is performed provided that the nonlinear terms have subcritical growth and (possible) variable sign; (iii) the presence of a bifurcation parameter. By studying the competition between the terms arising in the equation, the authors establish several existence and nonexistence results, as well as an exhaustive bifurcation description. The proofs combine variational techniques with related estimates of the associated energy functional.
[Teodora-Liliana Rădulescu (Craiova)]

MSC 2000:: *35J25 Second order elliptic equations, boundary value problems
35B09
35B32 Bifurcation (PDE)
35B40 Asymptotic behavior of solutions of PDE
35J60 Nonlinear elliptic equations
58E05 Abstract critical point theory

Keywords: Lane-Emden-Fowler equation; bifurcation problem; anisotropic continuous media; perturbation; positive solution

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