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Nodal solutions for critical Robin double phase problems with variable exponent

  • *Corresponding author: Patrick Winkert

    *Corresponding author: Patrick Winkert
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  • In this paper, we study a nonlinear double phase problem with variable exponent and critical growth on the boundary. The problem has in the reaction the combined effects of a Carathéodory perturbation defined only locally and of a critical term. The presence of the critical term does not permit to apply results of the critical point theory to the corresponding energy functional. Thus, we use appropriate cut-off functions and truncation techniques to work on an auxiliary coercive problem. In this way, we can use variational tools to get a sequence of sign changing solutions to our main problem. Further, we show that such a sequence converges to $ 0 $ in $ L^{\infty} $ and in the Musielak-Orlicz Sobolev space.

    Mathematics Subject Classification: 35A01, 35D30, 35J60, 35J62, 35J66.


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