Calculus of Variations and Geometric Measure Theory

A. Maione - D. Mugnai - E. Vecchi

Variational methods for nonpositive mixed local-nonlocal operators

created by maione on 29 Jul 2022
modified on 01 Jun 2023


Published Paper

Inserted: 29 jul 2022
Last Updated: 1 jun 2023

Journal: Fractional Calculus and Applied Analysis
Volume: 26
Number: 3
Pages: 943-961
Year: 2023
Doi: 10.1007/s13540-023-00147-2

ArXiv: 2207.14008 PDF


We prove the existence of a weak solution for boundary value problems driven by a mixed local--nonlocal operator. The main novelty is that such an operator is allowed to be nonpositive definite.

Keywords: Variational methods, Operators of mixed order, Saddle Point Theorem, Linking Theorem, asymptotically linear growth, superlinear and subcritical growth