Positive ground state of coupled systems of Schrödinger equations in R2 involving critical exponential growth

Ó, João Marcos do; Albuquerque, José Carlos de

doi:10.1002/mma.4498

Cited by 10 publications

(1 citation statement)

References 31 publications

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“…In [16,17], the authors studied the existence of positive ground states for (1.4) when N = 2 and f, g have exponential growth. For the case N ≥ 2 we refer the reader to [3, 5, 10-12, 22, 28, 29] and references therein.…”

Section: Introductionmentioning

confidence: 99%

Positive Ground States for a Class of Superlinear -Laplacian Coupled Systems Involving Schrödinger Equations

Albuquerque

Silva

2019

J. Aust. Math. Soc.

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We study the existence of positive ground state solutions for the following class of (p, q)-Laplacian coupled systemswhere N ≥ 3 and 1 < p ≤ q < N . Here the coefficient λ(x) of the coupling term is related with the potentials by the condition |λ(x)| ≤ δa(x) α/p b(x) β/q where δ ∈ (0, 1) and α/p + β/q = 1. We deal with periodic and asymptotically periodic potentials. The nonlinear terms f (s), g(s) are "superlinear" at 0 and at ∞ and are assumed without the well known Ambrosetti-Rabinowitz condition at infinity. Thus, we have established the existence of positive ground states solutions for a large class of nonlinear terms and potentials. Our approach is variational and based on minimization technique over the Nehari manifold.1991 Mathematics Subject Classification. 35J47, 35B09, 35J50, 35J92.

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Section: Introductionmentioning

confidence: 99%

Positive Ground States for a Class of Superlinear -Laplacian Coupled Systems Involving Schrödinger Equations

Albuquerque

Silva

2019

J. Aust. Math. Soc.

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Existence of solution to singular Schrödinger systems involving the fractional p‐Laplacian with Trudinger–Moser nonlinearity in ℝN

Thin

2021

Math Methods in App Sciences

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In this paper, we study the existence of weak solution for singular fractional Schrödinger system in R N involving Trudinger-Moser nonlinearity as follows:where ), and H has exponential growth and does not satisfy the Ambrosetti-Rabinowitz condition. Note that our problem is the lack of compactness. First, we give a version of vanishing lemma due to Lions;using that result and a version of Mountain pass theorem without (PS) condition, we obtain the existence of nontrivial solution to the above system. When H satisfies the Ambrosetti-Rabinowitz condition, motivated by the work of Chen et al.,we study the existence of nontrivial solution to singular Schrödinger system involving the fractional (p 1 , p)-Laplace and Trudinger-Moser nonlinearity. In our best knowledge, this is the first time the above problems are studied.

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Existence and asymptotic behavior of ground states for linearly coupled systems involving exponential growth

Severo,

de Albuquerque,

Santos

2023

Annali di Matematica

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Positive ground state of coupled systems of Schrödinger equations in R2 involving critical exponential growth

Cited by 10 publications

References 31 publications

Positive Ground States for a Class of Superlinear -Laplacian Coupled Systems Involving Schrödinger Equations

Positive Ground States for a Class of Superlinear -Laplacian Coupled Systems Involving Schrödinger Equations

Existence of solution to singular Schrödinger systems involving the fractional p‐Laplacian with Trudinger–Moser nonlinearity in ℝN

Existence and asymptotic behavior of ground states for linearly coupled systems involving exponential growth

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