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Combined effects in nonlinear problems arising in the study of anisotropic continuous media. (English) Zbl 1237.35043

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.

MSC:

35J25 Boundary value problems for second-order elliptic equations
35B09 Positive solutions to PDEs
35B32 Bifurcations in context of PDEs
35B40 Asymptotic behavior of solutions to PDEs
35J60 Nonlinear elliptic equations
58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
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