Geodesic
Existence of solutions to indefinite quasilinear elliptic problems of $p$-$q$-Laplacian type
Electronic Journal of Differential Equations, Tome 2010 (2010).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We study the indefinite quasilinear elliptic problem $$\displaylines{ -\Delta u-\Delta _{p}u=a(x)|u|^{q-2}u-b(x)|u|^{s-2}u \quad\hbox{in }\Omega , \cr u=0\quad\hbox{on }\partial \Omega , }$$ where $\Omega $ is a bounded domain in $\mathbb{R}^{N}, N\geq 2$, with a sufficiently smooth boundary, $q,s$ are subcritical exponents, $a(\cdot)$ changes sign and $b(x)\geq 0$ a.e. in $\Omega $. Our proofs are variational in character and are based either on the fibering method or the mountain pass theorem.
Classification : 35J60, 35J62, 35J92
Keywords: indefinite quasilinear elliptic problems, subcritical nonlinearities, p-Laplacian, p-q-Laplacian, fibering method, mountain pass theorem 
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     author = {Sidiropoulos, Nikolaos E.},
     title = {Existence of solutions to indefinite quasilinear elliptic problems of $p$-$q${-Laplacian} type},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2010},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2010__2010__a195/}
}
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Sidiropoulos, Nikolaos E. Existence of solutions to indefinite quasilinear elliptic problems of $p$-$q$-Laplacian type. Electronic Journal of Differential Equations, Tome 2010 (2010). http://geodesic.mathdoc.fr/item/EJDE_2010__2010__a195/