Geodesic
Existence of weak solutions for a $p(x)$-Laplacian equation via topological degree
Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 59 (2022), pp. 15-24

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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.
Keywords: weak solution, Dirichlet boundary condition, variable exponent Sobolev space, topological degree, $p(x)$-Laplacian. 
@article{IIMI_2022_59_a1,
     author = {M. Ait Hammou and E. H. Rami},
     title = {Existence of weak solutions for a $p(x)${-Laplacian} equation via topological degree},
     journal = {Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta},
     pages = {15--24},
     publisher = {mathdoc},
     volume = {59},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IIMI_2022_59_a1/}
}
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M. Ait Hammou; E. H. Rami. Existence of weak solutions for a $p(x)$-Laplacian equation via topological degree. Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 59 (2022), pp. 15-24. http://geodesic.mathdoc.fr/item/IIMI_2022_59_a1/