Work

The effect of the weight function on the number of solutions for double phase problems in $$\mathbb {R}^N$$

Year: 2025

Type: article

Abstract: In this paper we deal with quasilinear elliptic equations of the form $$\begin{aligned} -\operatorname {div}\left( |\nabla u|^{p-2}\nabla u+a(\varepsilon x)|\nabla u|^{q-2}\nabla u \right) +|u|^{p-2} u+a(\varepsilon x)|u|^{q-2}u&=f(u) \end{aligned}$$ - div | ∇ u | p - 2 ∇ u + a ( ε x ) | ∇ u | q - 2 ∇ u + | u | p - 2 u + a ( ε x ) | u | q - 2 u = f ( u ) in $$\mathbb {R}^N$$ R N , where $$0 \le a(\cdot )\in C\left( \mathbb {R}^N\right) \cap L^{\infty }\left( \mathbb {R}^N\right) $$ 0 ≤ a ( · ) ∈ C R N ∩ L ∞ R N , $$1 1 < p < N , $$p p < q < p ∗ = Np

Source: Revista Matemática Complutense

DOI: 10.1007/s13163-025-00556-2

Authors: Wulong Liu, Patrick Winkert

Institutions: Yantai University, Technische Universität Berlin

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funders: National Natural Science Foundation of China, Technische Universität Berlin