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Nonhomogeneous equations with critical exponential growth and lack of compactness

Figueiredo Giovany M., Radulescu Vicentiu D.

Opuscula Mathematica

2020

Vol. 40, no. 1

71--92

We study the existence and multiplicity of positive solutions for the following class of quasilinear problems [formula] where e∈ is a positive parameter. We assume that [formula] is a continuous potential and ƒ : R → R is a smooth reaction term with critical exponential growth.