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Low and high perturbations of nonhomogeneous eigenvalue problems with absorption
Rǎdulescu, Vicenţiu, 1958-
We are concerned with the mathematical analysis of a class of nonlinear eigenvalue problems driven by a nonhomogeneous differential operator. The features of this paper are the presence of an ...absorption term and the lack of compactness due to the study in the whole Euclidean space. The main result establishes the following properties: (i) the problem does not have solutions in the case of low perturbations of the reaction; (ii) the problem admits at least two nontrivial entire solutions in the case of high perturbations of the reaction. In both cases, the perturbations is considered in terms of the values of a suitable positive parameter. The proofs rely on simple variational methods and the arguments developed in this paper can be extended to other classes of nonlinear eigenvalue problems with nonstandard growth.
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