Ground state solutions for a kind of superlinear elliptic equations with variable exponent
| Autor: | Bosheng Xiao, Qiongfen Zhang |
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| Jazyk: | angličtina |
| Rok vydání: | 2024 |
| Předmět: | |
| Zdroj: | Boundary Value Problems, Vol 2024, Iss 1, Pp 1-23 (2024) |
| Druh dokumentu: | article |
| ISSN: | 1687-2770 |
| DOI: | 10.1186/s13661-023-01809-z |
| Popis: | Abstract In this paper, we focus on the existence of ground state solutions for the p ( x ) $p(x)$ -Laplacian equation { − Δ p ( x ) u + λ | u | p ( x ) − 2 u = f ( x , u ) + h ( x ) in Ω , u = 0 , on ∂ Ω . $$ \textstyle\begin{cases} -\Delta _{p(x)}u+\lambda \vert u \vert ^{p(x)-2}u=f(x,u)+h(x) \quad \text{in } \Omega , \\ u=0,\quad \text{on }\partial \Omega . \end{cases} $$ Using the constraint variational method, quantitative deformation lemma, and strong maximum principle, we proved that the above problem admits three ground state solutions, especially speaking, one solution is sign-changing, one is positive, and one is negative. Our results improve on those existing in the literature. |
| Databáze: | Directory of Open Access Journals |
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