Coercive and noncoercive elliptic problems with variable exponent Laplacian under Robin boundary conditions-Reference-Cited by-同舟云学术

Coercive and noncoercive elliptic problems with variable exponent Laplacian under Robin boundary conditions

Published:2022-12-01 Issue:6 Volume:72 Page:1541-1550
ISSN:0139-9918
Container-title:Mathematica Slovaca
language:en
Short-container-title:

Author:

Dammak Makkia¹²,Ali Abir Amor Ben³

Affiliation:

1. Department of Mathematics College of Science , Taibah University , Al-Madinah Al-Munawarah , Saudi Arabia

2. Department of Mathematics Faculty of Sciences of Sfax , University of Sfax , Sfax , Tunisia

3. Department of Mathematics Faculty of Sciences of Tunis , University of Tunis El Manar , Tunis , Tunisia

Abstract

Abstract In the present paper, we study the existence as well as the non-existence of some positive solutions for the equation −Δ p(x) u = λ k(x) uq ± h(x) ur under Robin boundary condition in a regular open bounded domain Ω of ℝ N , N ≥ 2. Δ p(x) is the p(x)-Laplacian operator where p ∈ C 1(Ω) and p > 1. Our proofs are based on the sub solution-super solution method and also on variational arguments.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/ms-2022-0105/pdf

Reference19 articles.

1. Alsaedi, A.—Ahmad, B.: Anisotropic problems with unbalanced growth, Adv. Nonlinear Anal. 9 (2020), 1504–1515.

2. Chandrasekhar, S.: An Introduction to the Study of Stellar Structure, Dover Books on Astronomy, 1985.

3. Deng, S. G.: Positive solutions for Robin problem involving the p(x)-Laplacian, J. Math. Anal. Appl. 360 (2009), 548–560.

4. Deng, S. G.—Wang, Q.—Cheng, S.: On the p(x)-Laplacian Robin eigenvalue problem, Appl. Math. Comput. 15(17) (2011), 5643–5649.

5. Fan, X. L.—Zhao, D: On the spaces Wk,p(x)(Ω) and Lp(x)(Ω), J. Math. Anal. Appl. 263 (2001), 424–446.