Ukr. Mat. Zh. - 2017. - 69, № 9. - pp. 1257-1265
We give some congruences involving $q$-harmonic numbers and alternating $q$-harmonic numbers of order $m$. Some of them are $q$-analogues of several known congruences.
Ukr. Mat. Zh. - 2014. - 66, № 12. - pp. 1676-1693
We establish the existence of at least three solutions for elliptic problems driven by a p(x)-Laplacian. The existence of at least one nontrivial solution is also proved. The approaches are based on the variational methods and critical-point theory.