Perturbations of nonlinear eigenvalue problems
Copyright policy )Perturbations of nonlinear eigenvalue problems
We consider perturbations of nonlinear eigenvalue problems driven by a nonhomogeneous differential operator plus an indefinite potential. We consider both sublinear and superlinear perturbations and we determine how the set of positive solutions changes as the real parameter $��$ varies. We also show that there exists a minimal positive solution $\overline{u}_��$ and determine the monotonicity and continuity properties of the map $��\mapsto\overline{u}_��$. Special attention is given to the particular case of the $p$-Laplacian.
arXiv admin note: text overlap with arXiv:1804.10003
- University of Ljubljana Slovenia
Variational methods for second-order elliptic equations, sublinear perturbation, sublinear and superlinear perturbation, 35J20, 35J60, nonlinear maximum principle, superlinear perturbation, comparison principle, info:eu-repo/classification/udc/517.956, Nonlinear elliptic equations, Mathematics - Analysis of PDEs, FOS: Mathematics, nonlinear regularity, minimal positive solution, nonhomogeneous differential operator, Analysis of PDEs (math.AP)
Variational methods for second-order elliptic equations, sublinear perturbation, sublinear and superlinear perturbation, 35J20, 35J60, nonlinear maximum principle, superlinear perturbation, comparison principle, info:eu-repo/classification/udc/517.956, Nonlinear elliptic equations, Mathematics - Analysis of PDEs, FOS: Mathematics, nonlinear regularity, minimal positive solution, nonhomogeneous differential operator, Analysis of PDEs (math.AP)
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