We consider the fractional relativistic Schrödinger-Choquard equation (equation presented), where ϵ > 0 is a small parameter, s (0, 1), m > 0, N > 2s, μ (0, 2s), (-δ + m2)s is the fractional relativistic Schrödinger operator, V: ℝN → ℝ is a continuous potential having a local minimum, f: ℝ → ℝ is a continuous nonlinearity with subcritical growth at infinity and F(t) =f0tf(τ)dτ. Exploiting appropriate variational arguments, we construct a family of solutions concentrating around the local minimum of V as ϵ → 0.

Concentration phenomena for the fractional relativistic Schrödinger-Choquard equation / Ambrosio, V.. - In: COMMUNICATIONS IN CONTEMPORARY MATHEMATICS. - ISSN 0219-1997. - 26:9(2024). [10.1142/S021919972350061X]

Concentration phenomena for the fractional relativistic Schrödinger-Choquard equation

Ambrosio V.
2024-01-01

Abstract

We consider the fractional relativistic Schrödinger-Choquard equation (equation presented), where ϵ > 0 is a small parameter, s (0, 1), m > 0, N > 2s, μ (0, 2s), (-δ + m2)s is the fractional relativistic Schrödinger operator, V: ℝN → ℝ is a continuous potential having a local minimum, f: ℝ → ℝ is a continuous nonlinearity with subcritical growth at infinity and F(t) =f0tf(τ)dτ. Exploiting appropriate variational arguments, we construct a family of solutions concentrating around the local minimum of V as ϵ → 0.
2024
Choquard equation; extension method; Fractional relativistic Schrödinger operator; variational methods
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11566/348497
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