Sharp Existence of Ground States Solutions for a Class of Elliptic Equations with Mixed Local and Nonlocal Operators and General Nonlinearity

Tingjian Luo () and Qihuan Xie
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Tingjian Luo: School of Mathematics and Information Sciences, Guangzhou University, Guangzhou 510006, China
Qihuan Xie: School of Mathematics and Information Sciences, Guangzhou University, Guangzhou 510006, China

Mathematics, 2023, vol. 11, issue 16, 1-15

Abstract: In this paper, we study the existence/non-existence of ground states for the following type of elliptic equations with mixed local and nonlocal operators and general nonlinearity: ( − ▵ ) s u − ▵ u + λ u = f ( u ) , x ∈ R N , which is driven by the superposition of Brownian and Lévy processes. By considering a constrained variational problem, under suitable assumptions on f , we manage to establish a sharp existence of the ground state solutions to the equation considered. These results improve the ones in the existing reference.

Keywords: constrained variational method; mixed local and nonlocal operators; sharp existence; general nonlinearity (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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