| Abstract: |
| The importance of studying problems involving $(p,q)$ operators, or operators with non-standard growth conditions, begins with the pioneering papers of Marcellini and Zhikov. Since then the subject has been attracting increasing attention on existence, regularity and qualitative properties of solutions of different problems. The talk is based on very recent results contained in a series of papers. In particular, existence of nontrivial entire solutions for critical Hardy quasilinear systems, driven by general $(p,q)$ elliptic operators of Marcellini types, are briefly presented. The results also raise, and leave open, a number of other intriguing questions. |
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