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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.

Isotropic and anisotropic double-phase problems: old and new

Radulescu Vicentiu D.

Opuscula Mathematica

2019

Vol. 39, no. 2

259--279

We are concerned with the study of two classes of nonlinear problems driven by differential operators with unbalanced growth, which generalize the (p, q)- and (p(x),q(x))-Laplace operators. The associated energy is a double-phase functional, either isotropic or anisotropic. The content of this paper is in relationship with pioneering contributions due to P. Marcelimi and G. Mingione.