We consider an anisotropic (Formula presented.) -equation, with a parametric and superlinear reaction term. We show 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.
Papageorgiou N.S., Repovs D.D., Vetro C. (2021). Constant sign and nodal solutions for parametric anisotropic (p,2)-equations. APPLICABLE ANALYSIS, 1-18 [10.1080/00036811.2021.1971199].
Constant sign and nodal solutions for parametric anisotropic (p,2)-equations
Vetro C.
2021-01-01
Abstract
We consider an anisotropic (Formula presented.) -equation, with a parametric and superlinear reaction term. We show 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.
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