Some nonlinear problems for the superposition of fractional operators with Neumann boundary conditions
arxiv(2024)
摘要
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.
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