Geodesic
General quasilinear problems involving $p(x)$-Laplacian with Robin boundary condition
Ural mathematical journal, Tome 6 (2020) no. 1, pp. 30-41

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This paper deals with the existence and multiplicity of solutions for a class of quasilinear problems involving $p(x)$-Laplace type equation, namely \begin{equation*}\label{E11} \left\{\begin{array}{lll} -\mathrm{div}\, (a(| \nabla u|^{p(x)})| \nabla u|^{p(x)-2} \nabla u)= \lambda f(x,u)\text{in}\Omega,\\ n\cdot a(| \nabla u|^{p(x)})| \nabla u|^{p(x)-2} \nabla u +b(x)|u|^{p(x)-2}u=g(x,u) \text{on}\partial\Omega. \end{array}\right. \end{equation*} Our technical approach is based on variational methods, especially, the mountain pass theorem and the symmetric mountain pass theorem.
Keywords: $p(x)$-Laplacian, Mountain pass theorem, Critical point theory.
Mots-clés : Multiple solutions 
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     author = {Hassan Belaouidel and Anass Ourraoui and Najib Tsouli},
     title = {General quasilinear problems involving $p(x)${-Laplacian} with {Robin} boundary condition},
     journal = {Ural mathematical journal},
     pages = {30--41},
     publisher = {mathdoc},
     volume = {6},
     number = {1},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UMJ_2020_6_1_a2/}
}
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Hassan Belaouidel; Anass Ourraoui; Najib Tsouli. General quasilinear problems involving $p(x)$-Laplacian with Robin boundary condition. Ural mathematical journal, Tome 6 (2020) no. 1, pp. 30-41. http://geodesic.mathdoc.fr/item/UMJ_2020_6_1_a2/