Existence of weak solutions for a $p(x)$-Laplacian equation via topological degree

M. Ait Hammou ; E. H. Rami

Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 59 (2022), pp. 15-24.

Résumé

We consider the $p(x)$-Laplacian equation with a Dirichlet boundary value condition \begin{equation*} \begin{cases} -\Delta_{p(x)}(u)+|u|^{p(x)-2}u= g(x,u,\nabla u), \in\Omega,\\ u=0, \in\partial\Omega, \end{cases} \end{equation*} Using the topological degree constructed by Berkovits, we prove, under appropriate assumptions, the existence of weak solutions for this equation.

Détail

Keywords: weak solution, Dirichlet boundary condition, variable exponent Sobolev space, topological degree, $p(x)$-Laplacian.

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