On a weighted problem of p-biharmonic type in the unit ball of R^N with exponential growth non linearity
DOI:
https://doi.org/10.12775/TMNA.2024.042Słowa kluczowe
Adam's inequality, nonlinearity of exponential growth, mountain pass method, compactness level, Nehari manifoldAbstrakt
In this paper, we are concerned with the existence of a ground state solution for a logarithmic weighted p-biharmonic equation under Dirichlet boundary conditions in the unit ball $B$ of $\mathbb{R}^{N}$. The reaction term of the equation is assumed to have exponential growth, in view of Adams' type inequalities. It is proved that there is a ground state solution using min-max techniques and the Nehari method. The associated energy functional loses compactness at a certain level. An appropriate asymptotic condition allows us to bypass the non-compactness levels of the functional.Bibliografia
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