Positive ground state of coupled systems of Schrödinger equations in
involving critical exponential growth |
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Authors: | João Marcos do Ó José Carlos de Albuquerque |
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Institution: | Department of Mathematics, Federal University of Paraíba, Jo?o Pessoa, PB, Brazil |
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Abstract: | In this paper, we study the existence of a positive ground state solution to the following coupled system of nonlinear Schrödinger equations: where the nonlinearities f1(x,s) and f2(x,s) are superlinear at infinity and have exponential critical growth of the Trudinger‐Moser type. The potentials V1(x) and V2(x) are nonnegative and satisfy a condition involving the coupling term λ(x), namely, λ(x)2<δ2V1(x)V2(x) for some 0<δ<1. For this purpose, we use the minimization technique over the Nehari manifold and strong maximum principle to get a positive ground state solution. Moreover, by using a bootstrap argument and Lq‐estimates, we get regularity and asymptotic behavior. |
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Keywords: | critical growth ground states lack of compactness Nehari manifold nonlinear Schrö dinger equations trudinger‐moser |
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