Publications of Stancu-Dumitru, Denisa

Equations involving a variable exponent Grushin-type operator

In this paper we define a Grushin-type operator with a variable exponent growth and establish existence results for an equation involving such an operator. A suitable function space setting is introduced. Regarding the tools used in proving the existence of solutions for the equation analysed here, they rely on the critical point theory combined with adequate variational techniques.

On a degenerate and singular elliptic equation with critical exponent and non-standard growth conditions

In this paper we study a class of degenerate and singular elliptic equations involving critical exponents and non-standard growth conditions in the whole space RN. We show the existence of at least one nontrivial solution using as main argument Ekeland’s variational principle.

On an eigenvalue problem involving the p(x)-Laplace operator plus a non-local term

We study an eigenvalue problem involving variable exponent growth conditions and a non-local term, on a bounded domain Ω ⊂ RN . Using adequate variational techniques, mainly based on the mountain-pass theorem of A. Ambrosetti and P. H. Rabinowitz, we prove the existence of a continuous family of eigenvalues lying in a neighborhood at the right of the origin.