On a Class of Parametric (p, 2)-equations

• Published in: Applied mathematics & optimization Vol. 75; no. 2; pp. 193 - 228
• Main Authors: Papageorgiou, Nikolaos S., Rădulescu, Vicenţiu D., Repovš, Dušan D.
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.04.2017; Springer Nature B.V; Springer Verlag (Germany)
• Subjects: Analysis of PDEs; Applications of mathematics; Applied mathematics; Banach spaces; Calculus of Variations and Optimal Control; Optimization; Control; Eigenvalues; Mathematical analysis; Mathematical and Computational Physics; Mathematical Methods in Physics; Mathematical models; Mathematics; Mathematics and Statistics; Numerical and Computational Physics; Operators (mathematics); Optimization; Ordinary differential equations; Parameters; Parametric equations; Partial differential equations; Simulation; Studies; Systems Theory; Texts; Theoretical; 35J20; Local minimizer; 58E05; Nonlinear maximum principle; 35J60; Critical group; Constant sign and nodal solutions; Near resonance
• ISSN: 0095-4616; 1432-0606
• DOI: 10.1007/s00245-016-9330-z

We consider parametric equations driven by the sum of a p -Laplacian and a Laplace operator (the so-called ( p , 2)-equations). We study the existence and multiplicity of solutions when the parameter λ > 0 is near the principal eigenvalue λ ^ 1 ( p ) > 0 of ( - Δ p , W 0 1 , p ( Ω ) ) . We prove multiplicity results with precise sign information when the near resonance occurs from above and from below of λ ^ 1 ( p ) > 0 .