Constant sign and nodal solutions for parametric anisotropic ▫$(p, 2)$▫-equations

Papageorgiou, Nikolaos, 1958- ; Repovš, Dušan, 1954- ; Vetro, Calogero

COBISS.SI-ID: 76549635

We consider an anisotropic (p, 2)-equation, with a parametric and superlinear reaction term.Weshow that for all small values of the parameter the problem has at least five nontrivial smooth solutions, four with constant sign and the fifth nodal (sign-changing). The proofs use tools from critical point theory, truncation and comparison techniques, and critical groups.