### Higher order nonlinear degenerate elliptic problems with weak monotonicity.

Akdim, Youssef, Azroul, Elhoussine, Rhoudaf, Mohamed (2006)

Electronic Journal of Differential Equations (EJDE) [electronic only]

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Akdim, Youssef, Azroul, Elhoussine, Rhoudaf, Mohamed (2006)

Electronic Journal of Differential Equations (EJDE) [electronic only]

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Akdim, Y., Azroul, E., Benkirane, A. (2001)

Electronic Journal of Differential Equations (EJDE) [electronic only]

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Akdim, Youssef, Azroul, Elhoussine, Benkirane, Abdelmoujib (2002)

Electronic Journal of Differential Equations (EJDE) [electronic only]

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Albo Carlos Cavalheiro (2014)

Archivum Mathematicum

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In this article we are interested in the existence and uniqueness of solutions for the Dirichlet problem associated with the degenerate nonlinear elliptic equations $$\begin{array}{cc}\hfill \Delta \left(v\left(x\right)\phantom{\rule{0.166667em}{0ex}}{\left|\Delta u\right|}^{p-2}\Delta u\right)& -\sum _{j=1}^{n}{D}_{j}\left[\omega \left(x\right){\mathcal{A}}_{j}(x,u,\nabla u)\right]\hfill \\ \hfill =& \phantom{\rule{4pt}{0ex}}{f}_{0}\left(x\right)-\sum _{j=1}^{n}{D}_{j}{f}_{j}\left(x\right)\phantom{\rule{0.166667em}{0ex}},\phantom{\rule{1.0em}{0ex}}in\phantom{\rule{1.0em}{0ex}}\Omega \hfill \end{array}$$ in the setting of the weighted Sobolev spaces.

Youssef Akdim, Elhoussine Azroul, Abdelmoujib Benkirane (2004)

Revista Matemática Complutense

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In this paper we study the existence of solutions for quasilinear degenerated elliptic operators A(u) + g(x,u,∇u) = f, where A is a Leray-Lions operator from W (Ω,ω) into its dual, while g(x,s,ξ) is a nonlinear term which has a growth condition with respect to ξ and no growth with respect to s, but it satisfies a sign condition on s. The right hand side f is assumed to belong either to W(Ω,ω*) or to L(Ω).

Wang, Z., Liu, L. (2010)

Annals of Functional Analysis (AFA) [electronic only]

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Chen, Zuchi, Xuan, Benjin (2002)

Electronic Journal of Differential Equations (EJDE) [electronic only]

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Rakotondratsimba, Y. (1998)

Georgian Mathematical Journal

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Youssef Akdim, Elhoussine Azroul, Abdelmoujib Benkirane (2003)

Annales mathématiques Blaise Pascal

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An existence theorem is proved, for a quasilinear degenerated elliptic inequality involving nonlinear operators of the form $Au+g(x,u,\nabla u)$, where $A$ is a Leray-Lions operator from ${W}_{0}^{1,p}(\Omega ,w)$ into its dual, while $g(x,s,\xi )$ is a nonlinear term which has a growth condition with respect to $\xi $ and no growth with respect to $s$, but it satisfies a sign condition on $s$, the second term belongs to ${W}^{-1,{p}^{\prime}}(\Omega ,{w}^{*})$.

Benboubker, Mohamed Badr, Azroul, Elhoussine, Barbara, Abdelkrim (2011)

Electronic Journal of Differential Equations (EJDE) [electronic only]

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