Three solutions to a Steklov problem involving the weighted $p(\cdot)$-Laplacian

Ismail Aydin; Cihan Unal

doi:10.1216/rmj.2021.51.67

Abstract

We study a nonlinear Steklov boundary-value problem involving the weighted $p (\cdot)$ -Laplacian. Using the Ricceri’s variational principle, we obtain the existence of at least three weak solutions in double weighted variable exponent Sobolev space.

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Ismail Aydin. Cihan Unal. "Three solutions to a Steklov problem involving the weighted $p(\cdot)$-Laplacian." Rocky Mountain J. Math. 51 (1) 67 - 76, February 2021. https://doi.org/10.1216/rmj.2021.51.67

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Received: 19 May 2020; Revised: 5 August 2020; Accepted: 12 August 2020; Published: February 2021

First available in Project Euclid: 28 May 2021

Digital Object Identifier: 10.1216/rmj.2021.51.67

Subjects:

Primary: 35D30 , 46E35

Secondary: 35J60 , 35J70

Keywords: $p(\cdot)$-Laplacian , Ricceri's variational principle , Steklov problem , weighted variable exponent Sobolev spaces

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