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Article Dans Une Revue Asymptotic Analysis Année : 2023

On periodic and compactly supported least energy solutions to semilinear elliptic equations with non-Lipschitz nonlinearity

Résumé

We discuss the existence and non-existence of periodic in one variable and compactly supported in the other variables least energy solutions for equations with non-Lipschitz nonlinearity of the form: − Δ u = λ u p − u q in R N + 1 , where 0 < q < p < 1 and λ ∈ R. The approach is based on the Nehari manifold method supplemented by a one-sided constraint given through the functional of the suitable Pohozaev identity. The limit value of the parameter λ, where the approach is applicable, corresponds to the existence of periodic in one variable and compactly supported in the other variables least energy solutions. This value is found through the extrem values of nonlinear generalized Rayleigh quotients and the so-called curve of the critical exponents of p, q. Important properties of the solutions are derived for suitable ranges of the parameters, such as that they are not trivial with respect to the periodic variable and do not coincide with compactly supported solutions on the entire space R N + 1 .

Dates et versions

hal-04298177 , version 1 (21-11-2023)

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Citer

Jacques Giacomoni, Yavdat Il’yasov, Deepak Kumar. On periodic and compactly supported least energy solutions to semilinear elliptic equations with non-Lipschitz nonlinearity. Asymptotic Analysis, 2023, pp.1-25. ⟨10.3233/ASY-231878⟩. ⟨hal-04298177⟩
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