On asymptotically linear elliptic problems

2022/10/11 by Nascimento, José Roberto, Pimenta, Marcos Tadeu O., Júnior, João R. Santos
#35J15 #35J25 #35J61 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2210.05452

Abstract

In this paper we prove the existence of a signed ground state solution in the mountain pass level for a class of asymptotically linear elliptic problems, even when the nonlinearity is just continuous in the second variable. The (strongly) resonant and non-resonant cases are discussed. A multiplicity result is also proved when f is odd with respect to the second variable.

Related

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• Perturbed asymptotically linear problems
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• Asymptotic Estimates and Qualitatives Properties of an Elliptic Problem in Dimension Two
• Ground state solutions for a semilinear elliptic problem with critical-subcritical growth