Some nonlinear problems for the superposition of fractional operators with Neumann boundary conditions

Abstract

We discuss the existence theory of a nonlinear problem of nonlocal type subject to Neumann boundary conditions. Differently from the existing literature, the elliptic operator under consideration is obtained as a superposition of operators of mixed order. The setting that we introduce is very general and comprises, for instance, the sum of two fractional Laplacians, or of a fractional Laplacian and a Laplacian, as particular cases (the situation in which there are infinitely many operators, and even a continuous distribution of operators, can be considered as well). New bits of functional analysis are introduced to deal with this problem. An eigenvalue analysis divides the existence theory into two streams, one related to a Mountain Pass method, the other to a Linking technique.

References in corpus (5)

• An existence theory for superposition operators of mixed order subject to jumping nonlinearities
• An existence theory for nonlinear superposition operators of mixed fractional order
• A general theory for the $(s,p)$-superposition of nonlinear fractional operators
• The Neumann condition for the superposition of fractional Laplacians
• A multiplicity result for critical elliptic problems involving differences of local and nonlocal operators

Cited by in corpus (1)

• Logistic diffusion equations governed by the superposition of operators of mixed fractional order