Ukr. Mat. Zh. - 2015. - 67, № 6. - pp. 788-808
We study the existence of multiple solutions for a quasilinear elliptic system. Based on the Ambrosetti–Rabinowitz mountain-pass theorem and the Rabinowitz symmetric mountain-pass theorem, we establish several existence and multiplicity results for the solutions and G-symmetric solutions under certain suitable conditions.
Ukr. Mat. Zh. - 2012. - 64, № 6. - pp. 797-810
We consider a quasilinear elliptic system involving the critical Hardy - Sobolev exponent and Sobolev exponent. Using variational methods and analytic techniques, we establish the existence of positive solutions of the system.