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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:
35J25Second order elliptic equations, boundary value problems
35B09Positive solutions of PDE
35B32Bifurcation (PDE)
35B40Asymptotic behavior of solutions of PDE
35J60Nonlinear elliptic equations
58E05Abstract critical point theory
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