Nonlinear scalar field $$(p_{1}, p_{2})$$-Laplacian equations in $$\mathbb {R}^{N}$$: existence and multiplicity
Year: 2024
Type: article
Abstract: In this paper, we deal with the following class of $$(p_{1}, p_{2})$$ ( p 1 , p 2 ) -Laplacian problems: $$\begin{aligned} \left\{ \begin{array}{ll} -\Delta _{p_{1}}u-\Delta _{p_{2}}u= g(u) \text{ in } \mathbb {R}^{N},\\ u\in W^{1, p_{1}}(\mathbb {R}^{N})\cap W^{1, p_{2}}(\mathbb {R}^{N}), \end{array} \right. \end{aligned}$$ - Δ p 1 u - Δ p 2 u = g ( u ) in R N , u ∈ W 1 , p 1 ( R N ) ∩ W 1 , p 2 ( R N ) , where $$N\ge 2$$ N ≥ 2 , $$1 1 < p 1 < p 2 ≤ N , $$\Delta _{p_{i}}$$ Δ p i is the $$p_{i}$$ p i -Laplacian operator, for $$i=1, 2$$ i = 1 , 2 , and $$g:\mathbb {R}\rightarrow \mathbb {R}$$ g : R → R is a Berestycki-Lions type nonlinearity. Using appropriate variational arguments, we obtain the existence of a ground state solution. In particular, we provide three different approaches to deduce this result. Finally, we prove the ex
Author: Vincenzo Ambrosio
Institution: Marche Polytechnic University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
OpenAlex ID: W4402117963