- journal article metadata
European Mathematical Society Publishing House
2018-01-11 23:40:02
Zeitschrift für Analysis und ihre Anwendungen
Z. Anal. Anwend.
ZAA
0232-2064
1661-4534
Partial differential equations
Ordinary differential equations
Integral equations
Numerical analysis
10.4171/ZAA
http://www.ems-ph.org/doi/10.4171/ZAA
subscribers
European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society (from 2006)
37
2018
1
On the Robin Problem with Indefinite Weight in Sobolev Spaces with Variable Exponents
Khaled
Kefi
Université de Tunis, Tunisia
Robin problem, Ekeland's variational principle, generalized Sobolev spaces, weak solution
The present paper is concerned with a Robin problem involving an indefinite weight in Sobolev spaces with variable exponents \begin{equation*} \left\{\begin{alignedat}{2}-\text{ div}(|\nabla u|^{p(x)-2}\nabla u)&=\lambda V(x)|u|^{q(x)-2}u,& \quad x&\in\Omega\\ |\nabla u|^{p(x)-2} \frac{\partial u}{\partial n}+a(x)|u|^{p(x)-2}u&=0.&\quad x&\in\partial\Omega \end{alignedat}\right. \end{equation*} By means of the variational approach and Ekeland's principle, we establish that the above problem admits a non-trivial weak solution under appropriate conditions.
Partial differential equations
Functional analysis
25
38
10.4171/ZAA/1600
http://www.ems-ph.org/doi/10.4171/ZAA/1600
1
8
2018