Existence of Solution for a Class of Variational Inequality in Whole RN with Critical Growth: The Local Mountain Pass Case

Alves C.O.; Barros L.M.; Torres Ledesma C.E. · Mediterranean Journal of Mathematics (2023) · DOI: 10.1007/s00009-023-02450-x

Resumen

In this paper, we study the existence of solution for a class of variational inequality in whole RN where the nonlinearity has a critical growth for N≥ 2. By combining a penalization scheme found in del Pino and Felmer (Calc Var 4:121–137, 1996) with a penalization method due to Bensoussan and Lions (Applications des inéquations variationelles en contrôle stochastique. Dunod, Paris, 1978), we improve a recent result by Alves et al. (J Math Anal Appl 494:124672, 2021).

Instituciones: Universidad Nacional de Trujillo