On the Robin Problem with Indefinite Weight in Sobolev Spaces with Variable Exponents

Khaled Kefi

doi:10.4171/zaa/1600

JournalszaaVol. 37, No. 1pp. 25–38

On the Robin Problem with Indefinite Weight in Sobolev Spaces with Variable Exponents

Khaled Kefi
Northern Border University, Kingdom of Saudi Arabia

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Abstract

The present paper is concerned with a Robin problem involving an indefinite weight in Sobolev spaces with variable exponents

⎩ ⎨ ⎧ - div (∣\nabla u ∣^{p (x) - 2} \nabla u) ∣\nabla u ∣^{p (x) - 2} \frac{\partial u}{\partial n} + a (x) ∣ u ∣^{p (x) - 2} u = λV (x) ∣ u ∣^{q (x) - 2} u, = 0. x x \in Ω \in \partial Ω

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.

Cite this article

Khaled Kefi, On the Robin Problem with Indefinite Weight in Sobolev Spaces with Variable Exponents. Z. Anal. Anwend. 37 (2018), no. 1, pp. 25–38

DOI 10.4171/ZAA/1600