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On a Hamiltonian System with Critical Exponential Growth

  • Yony R. Santaria Leuyacc
  • Sergio H. Monari SoaresEmail author
Article
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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.

Keywords

Hamiltonian elliptic systems exponential growth Lorentz–Sobolev spaces 

Mathematics Subject Classification (2010)

Primary 35J47 35J50 Secondary 46E30 46E35 

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Yony R. Santaria Leuyacc
    • 1
  • Sergio H. Monari Soares
    • 1
    Email author
  1. 1.Instituto de Ciências Matemáticas e de ComputaçãoUniversidade de São PauloSão CarlosBrazil

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