Abstract
It is established existence of weak solution for a semilinear superlinear elliptic problems on bounded domains. The main feature of the paper is to prove that, for superlinear problems, the nonquadraticity condition introduced by Costa and Magalhães in (Nonlinear Anal. 23:1401–1412, 1994) is sufficient to get the compactness required by minimax procedures.
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The authors were partially supported by CNPq/Brazil under the grants 307327/2013-2 and 211623/2013-0, respectively.
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Dedicated to Prof. Djairo de Figueiredo on the occasion of his 80th birthday
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Furtado, M.F., Silva, E.D. (2015). Nonquadraticity condition on superlinear problems. In: Nolasco de Carvalho, A., Ruf, B., Moreira dos Santos, E., Gossez, JP., Monari Soares, S., Cazenave, T. (eds) Contributions to Nonlinear Elliptic Equations and Systems. Progress in Nonlinear Differential Equations and Their Applications, vol 86. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-19902-3_16
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