Abstract
In this work we investigate the existence and multiplicity of solutions for a class of nonlocal problems involving the fractional N/s-Laplacian and nonlinearities that may have exponential growth of Trudinger–Moser type. First, by using the constraint variational method, the quantitative deformation lemma and the fractional Trudinger–Moser inequality, we establish the existence of a least energy nodal solution. Next, minimax techniques are exploited to prove the existence of one nonnegative and of one nonpositive ground state solution. In a third stage, we show that the energy of the nodal solution is strictly larger than twice the ground state energy.
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The authors would like to express sincere thanks to the anonymous reviewers for their carefully reading of the manuscript with valuable corrections and suggestions.
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Research partially supported by CNPq Grants 309998/2020-4 and 310747/2019-8.
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de Souza, M., Severo, U.B. & do Rêgo, T.L.O. On solutions for fractional \(\pmb {N/s}\)-Laplacian equations involving exponential growth. Nonlinear Differ. Equ. Appl. 28, 60 (2021). https://doi.org/10.1007/s00030-021-00721-8
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DOI: https://doi.org/10.1007/s00030-021-00721-8