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Existence results for Navier problems with degenerated (p,q)-Laplacian and (p,q)-Biharmonic operators

Albo Carlos Cavalheiro 

In this article, we prove the existence

and uniqueness of  solutions for the Navier problem

$(P)\left\{ \begin{array}{llll} & {\Delta}{\big[}{\omega}(x)(\,{\vert{\Delta}u\vert}^{p-2}{\Delta}u + {\vert{\Delta}u\vert}^{q-2}{\Delta}u){\big]} -{\rm div}{\big[}{\omega}(x)(\,{\vert{\nabla}u\vert}^{p-2}{\nabla}u + {\vert{\nabla}u\vert}^{q-2}{\nabla}u){\big]}\\ & = f(x) - {\rm div}(G(x)),\ \ {\rm in} \ \ {\Omega}, \\ & u(x) = {\Delta}u= 0, \ \ {\rm in} \ \ {\partial\Omega}, \end{array} \right.$

\noindent where  $\Omega$ is a bounded open set of ${\real}^N$

($N\,{\geq}\,2$), $\displaystyle {\dfrac{f}{\omega}}\,{\in}\,L^{p\,'}(\Omega , \omega)$ and

$\displaystyle{\dfrac{G}{\omega}}\, {\in}\,[L^{q\,'}(\Omega , \omega)]^N$ .

Degenerate nonlinear ellliptic equations, , weighted Sobolev space
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Primary Language en Articles Orcid: 0000-0003-1337-1292Author: Albo Carlos Cavalheiro (Primary Author)Institution: State University of LondrinaCountry: Brazil Publication Date : August 31, 2018
 Bibtex @research article { rna430698, journal = {Results in Nonlinear Analysis}, issn = {}, eissn = {2636-7556}, address = {}, publisher = {Erdal KARAPINAR}, year = {2018}, volume = {1}, pages = {74 - 87}, doi = {}, title = {Existence results for Navier problems with degenerated (p,q)-Laplacian and (p,q)-Biharmonic operators}, key = {cite}, author = {Cavalheiro, Albo Carlos} } APA Cavalheiro, A . (2018). Existence results for Navier problems with degenerated (p,q)-Laplacian and (p,q)-Biharmonic operators. Results in Nonlinear Analysis , 1 (2) , 74-87 . Retrieved from https://dergipark.org.tr/en/pub/rna/issue/37067/430698 MLA Cavalheiro, A . "Existence results for Navier problems with degenerated (p,q)-Laplacian and (p,q)-Biharmonic operators". Results in Nonlinear Analysis 1 (2018 ): 74-87 Chicago Cavalheiro, A . "Existence results for Navier problems with degenerated (p,q)-Laplacian and (p,q)-Biharmonic operators". Results in Nonlinear Analysis 1 (2018 ): 74-87 RIS TY - JOUR T1 - Existence results for Navier problems with degenerated (p,q)-Laplacian and (p,q)-Biharmonic operators AU - Albo Carlos Cavalheiro Y1 - 2018 PY - 2018 N1 - DO - T2 - Results in Nonlinear Analysis JF - Journal JO - JOR SP - 74 EP - 87 VL - 1 IS - 2 SN - -2636-7556 M3 - UR - Y2 - 2018 ER - EndNote %0 Results in Nonlinear Analysis Existence results for Navier problems with degenerated (p,q)-Laplacian and (p,q)-Biharmonic operators %A Albo Carlos Cavalheiro %T Existence results for Navier problems with degenerated (p,q)-Laplacian and (p,q)-Biharmonic operators %D 2018 %J Results in Nonlinear Analysis %P -2636-7556 %V 1 %N 2 %R %U ISNAD Cavalheiro, Albo Carlos . "Existence results for Navier problems with degenerated (p,q)-Laplacian and (p,q)-Biharmonic operators". Results in Nonlinear Analysis 1 / 2 (August 2018): 74-87 . AMA Cavalheiro A . Existence results for Navier problems with degenerated (p,q)-Laplacian and (p,q)-Biharmonic operators. RNA. 2018; 1(2): 74-87. Vancouver Cavalheiro A . Existence results for Navier problems with degenerated (p,q)-Laplacian and (p,q)-Biharmonic operators. Results in Nonlinear Analysis. 2018; 1(2): 87-74.