Abstract
We are interested in finding nontrivial solutions for a Hamiltonian elliptic system in dimension two involving a potential function which can be coercive and nonlinearities that have maximal growth with respect to the Trudinger–Moser inequality. To establish the existence of solutions, we use variational methods combined with Trudinger–Moser type inequalities in Lorentz–Sobolev spaces and a finite-dimensional approximation.
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This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior – Brasil (CAPES) – Finance Code 001. The second author was partly supported by CNPq/Brazil.
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Leuyacc, Y.R.S., Soares, S.H.M. On a Hamiltonian System with Critical Exponential Growth. Milan J. Math. 87, 105–140 (2019). https://doi.org/10.1007/s00032-019-00294-3
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DOI: https://doi.org/10.1007/s00032-019-00294-3