Abstract
We study the nonlinear degenerate anisotropic problem
where \(\Omega \subset \mathbb R^N\) is a bounded domain with smooth boundary. The constant value of the boundary data is not specified, whereas the zero integral term corresponds to a no-flux boundary condition. In the case when \(|u|^{q(x)-2}u\) “dominates” the left-hand side, we show that a nontrivial solution exists for all positive values of \(\lambda \). If the term \(|u|^{q(x)-2}u\) is dominated by the left-hand side, we prove that a solution exists either for small or for large values of \(\lambda >0\). The proofs combine variational arguments with energy estimates.
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Afrouzi, G.A., Mirzapour, M. & Rădulescu, V.D. The variational analysis of a nonlinear anisotropic problem with no-flux boundary condition. RACSAM 109, 581–595 (2015). https://doi.org/10.1007/s13398-014-0202-6
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DOI: https://doi.org/10.1007/s13398-014-0202-6