In this paper, we investigate the existence of multiple solutions for the following two fractional problems: (equation present) where s ϵ (0,1), N > 2 , Ω is a smooth bounded domain of ℝN, and f : Ω × ℝ → ℝ is a superlinear continuous function which does not satisfy the well-known Ambrosetti-Rabinowitz condition. Here (- ΔΩ)s is the spectral Laplacian and (-ΔℝN) s is the fractional Laplacian in ℝN. By applying variational theorems of mixed type due to Marino and Saccon and the Linking Theorem, we prove the existence of multiple solutions for the above problems.
Multiple solutions for superlinear fractional problems via theorems of mixed type
Ambrosio V.
2018-01-01
Abstract
In this paper, we investigate the existence of multiple solutions for the following two fractional problems: (equation present) where s ϵ (0,1), N > 2 , Ω is a smooth bounded domain of ℝN, and f : Ω × ℝ → ℝ is a superlinear continuous function which does not satisfy the well-known Ambrosetti-Rabinowitz condition. Here (- ΔΩ)s is the spectral Laplacian and (-ΔℝN) s is the fractional Laplacian in ℝN. By applying variational theorems of mixed type due to Marino and Saccon and the Linking Theorem, we prove the existence of multiple solutions for the above problems.File in questo prodotto:
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