Kirchhoff-Schrödinger equations in ℝ² with critical exponential growth and indefinite potential

2018/05/04 by Marcelo F. Furtado, Furtado, Marcelo F., Henrique Rennó Zanata +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Partial Differential Equations #Primary 35J60 #Secondary 35J50

paper · pdf · doi:10.48550/arxiv.1805.01587

openalex publication_date 2018/05/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We obtain the existence of ground state solution for the nonlocal problem m(∫_ℝ²(|∇ u|² + b(x)u²) \textrmdx)(-Δu + b(x)u) = A(x)f(u) \textrmin ℝ², where m is a Kirchhoff-type function, b may be negative and noncoercive, A is locally bounded and the function f has critical exponential growth. We also obtain new results for the classical Schrödinger equation, namely the local case m≡ 1. In the proofs we apply Variational Methods beside a new Trudinger-Moser type inequality.

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