Nontrivial solutions for nonlinear problems driven by a superposition of fractional p-Laplacians with Neumann boundary conditions

In this paper, we investigate existence results for nonlinear nonlocal problems governed by an operator obtained as a superposition of fractional $p$-Laplacians, subject to Neumann boundary conditions. A spectral analysis of the main operator leads us to apply different variational tools to establish our results. Specifically, we will use either the mountain pass method or the technique of linking over cones. Due to the generality of the setting, the resulting theory applies to a wide range of specific situations.

💡 Research Summary

The paper studies the existence of nontrivial weak solutions for a class of nonlinear nonlocal equations driven by a superposition of fractional p‑Laplacians together with the classical p‑Laplacian, under Neumann boundary conditions. The main operator is defined as
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