Year 2018, Volume 1, Issue 2, Pages 74 - 87 2018-08-31

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

Albo Carlos Cavalheiro [1]

23 51

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
Journal Section Articles
Authors

Orcid: 0000-0003-1337-1292
Author: Albo Carlos Cavalheiro (Primary Author)
Institution: State University of Londrina
Country: Brazil


Bibtex @research article { rna430698, journal = {Results in Nonlinear Analysis}, issn = {}, eissn = {2636-7556}, address = {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 http://dergipark.org.tr/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 <http://dergipark.org.tr/rna/issue/37067/430698>
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.