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 23 Mar 2023


Accepted Paper

Inserted: 29 jul 2022
Last Updated: 23 mar 2023

Journal: Fractional Calculus and Applied Analysis
Year: 2023

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