On solutions for a class of Kirchhoff systems involving critical growth in R 2
| Autor: | J.C. de Albuquerque, J.M. do Ó, E.O. dos Santos, U.B. Severo |
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| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | Asymptotic Analysis. 122:69-85 |
| ISSN: | 1875-8576 0921-7134 |
| DOI: | 10.3233/asy-201610 |
| Popis: | In this work we study the existence of solutions for the following class of elliptic systems involving Kirchhoff equations in the plane: m ( ‖ u ‖ 2 ) [ − Δ u + u ] = λ f ( u , v ) , x ∈ R 2 , ℓ ( ‖ v ‖ 2 ) [ − Δ v + v ] = λ g ( u , v ) , x ∈ R 2 , where λ > 0 is a parameter, m , ℓ : [ 0 , + ∞ ) → [ 0 , + ∞ ) are Kirchhoff-type functions, ‖ · ‖ denotes the usual norm of the Sobolev space H 1 ( R 2 ) and the nonlinear terms f and g have exponential critical growth of Trudinger–Moser type. Moreover, when f and g are odd functions, we prove that the number of solutions increases when the parameter λ becomes large. |
| Databáze: | OpenAIRE |
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