We consider a parametric Dirichlet problem driven by the sum of a p-Laplacian (p> 2) and a Laplacian (a (p, 2)-equation). The reaction consists of an asymmetric (p- 1) -linear term which is resonant as x→ - ∞, plus a concave term. However, in this case the concave term enters with a negative sign. Using variational tools together with suitable truncation techniques and Morse theory (critical groups), we show that when the parameter is small the problem has at least three nontrivial smooth solutions.

Papageorgiou N.S., Vetro C., Vetro F. (2020). (p, 2)-Equations with a Crossing Nonlinearity and Concave Terms. APPLIED MATHEMATICS AND OPTIMIZATION, 81(1), 221-251 [10.1007/s00245-018-9482-0].

(p, 2)-Equations with a Crossing Nonlinearity and Concave Terms

Vetro C.;
2020-01-01

Abstract

We consider a parametric Dirichlet problem driven by the sum of a p-Laplacian (p> 2) and a Laplacian (a (p, 2)-equation). The reaction consists of an asymmetric (p- 1) -linear term which is resonant as x→ - ∞, plus a concave term. However, in this case the concave term enters with a negative sign. Using variational tools together with suitable truncation techniques and Morse theory (critical groups), we show that when the parameter is small the problem has at least three nontrivial smooth solutions.
Settore MAT/05 - Analisi Matematica
https://link.springer.com/article/10.1007/s00245-018-9482-0
Papageorgiou N.S., Vetro C., Vetro F. (2020). (p, 2)-Equations with a Crossing Nonlinearity and Concave Terms. APPLIED MATHEMATICS AND OPTIMIZATION, 81(1), 221-251 [10.1007/s00245-018-9482-0].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/400184
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