Multiple perturbations of a singular eigenvalue problem. (English) Zbl 1328.35007
Summary: We study the perturbation by a critical term and a \((p - 1)\)-superlinear subcritical nonlinearity of a quasilinear elliptic equation containing a singular potential. By means of variational arguments and a version of the concentration-compactness principle in the singular case, we prove the existence of solutions for positive values of the parameter under the principal eigenvalue of the associated singular eigenvalue problem.
MSC:
| 35B33 | Critical exponents in context of PDEs |
| 35B38 | Critical points of functionals in context of PDEs (e.g., energy functionals) |
| 35P30 | Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs |
| 47J10 | Nonlinear spectral theory, nonlinear eigenvalue problems |
| 58E05 | Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces |
Keywords:
critical Sobolev exponent; indefinite singular potential; principal eigenvalue; concentration-compactness; singularityReferences:
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