Infinitely many weak solutions for p(x)-Laplacian-like problems with sign-changing potential
This study is concerned with the p(x)-Laplacian-like problems and arising from capillarity phenomena of the following type −div ��1 + |∇u| p(x) 1+|∇u| 2p(x) |∇u| p(x)−2∇u = λ f(x, u), in Ω, u = 0, on ∂Ω, where Ω is a bounded domain in RN with smooth boundary ∂Ω, p ∈ C(Ω), and the primitive of the no...
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Dokumentumtípus: | Folyóirat |
Megjelent: |
2020
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Sorozat: | Electronic journal of qualitative theory of differential equations
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Kulcsszavak: | Differenciálegyenlet |
doi: | 10.14232/ejqtde.2020.1.10 |
Online Access: | http://acta.bibl.u-szeged.hu/69514 |
Tartalmi kivonat: | This study is concerned with the p(x)-Laplacian-like problems and arising from capillarity phenomena of the following type −div ��1 + |∇u| p(x) 1+|∇u| 2p(x) |∇u| p(x)−2∇u = λ f(x, u), in Ω, u = 0, on ∂Ω, where Ω is a bounded domain in RN with smooth boundary ∂Ω, p ∈ C(Ω), and the primitive of the nonlinearity f of super-p + growth near infinity in u and is also allowed to be sign-changing. Based on a direct sum decomposition of a space W 1,p(x) 0 (Ω), we establish the existence of infinitely many solutions via variational methods for the above equation. Furthermore, our assumptions are suitable and different from those studied previously. |
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ISSN: | 1417-3875 |