Research Article | Open Access
Teodora-Liliana Dinu, "Nonlinear eigenvalue problems in Sobolev spaces with variable exponent", Journal of Function Spaces, vol. 4, Article ID 515496, 18 pages, 2006. https://doi.org/10.1155/2006/515496
Nonlinear eigenvalue problems in Sobolev spaces with variable exponent
We study the boundary value problem in , on , where is a smooth bounded domain in . We focus on the cases when , where for any . In the first case we show the existence of infinitely many weak solutions for any . In the second case we prove that if is large enough then there exists a nontrivial weak solution. Our approach relies on the variable exponent theory of generalized Lebesgue-Sobolev spaces, combined with a -symmetric version for even functionals of the Mountain Pass Lemma and some adequate variational methods.
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