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A continuous spectrum for nonhomogeneous differential operators in Orlicz-Sobolev spacesMihǎilescu, Mihai ; Rǎdulescu, Vicenţiu, 1958-We study the nonlinear eigenvalue problem ▫$-{\rm div}(a(|\nabla u|)\nabla u) = \lambda|u|^{q(x)-2}u$▫ in ▫$\Omega$▫, ▫$u=0$▫ on ▫$\partial\Omega$▫, where ▫$\Omega$▫ is a bounded open set in ... ▫$\mathbb R^N$▫ with smooth boundary, ▫$q$▫ is a continuous function, and ▫$a$▫ is a nonhomogeneous potential. We establish sufficient conditions on ▫$a$▫ and ▫$q$▫ such that the above nonhomogeneous quasilinear problem has continuous families of eigenvalues. The proofs rely on elementary variational arguments. The abstract results of this paper are illustrated by the cases ▫$a(t) = t^{p-2}\log (1+t^r)$▫ and ▫$a(t) = t^{p-2} [\log (1+t)]^{-1}$▫.Source: Mathematica Scandinavica. - ISSN 0025-5521 (Vol. 104, no. 1, 2009, str. 132-146)Type of material - article, component partPublish date - 2009Language - englishCOBISS.SI-ID - 15100505
Author
Mihǎilescu, Mihai |
Rǎdulescu, Vicenţiu, 1958-
Topics
matematika |
parcialne diferencialne enačbe |
nelinearni problem lastnih vrednosti |
zvezni spekter |
nehomogeni potencial |
mathematics |
partial differential equations |
nonlinear eigenvalue problem |
continuous spectrum |
nonhomogeneous potential
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Mihǎilescu, Mihai | ![]() |
Rǎdulescu, Vicenţiu, 1958- | 29964 |
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