We study distributional solutions of semilinear biharmonic equations of the type ∆2u+f(u)=0 onRN, where f is a continuous function satisfying f(t)t ≥ c|t|q+1 for all t ∈ R with c > 0 and q > 1. By using a new approach mainly based on careful choice of suitable weighted test functions and a new version of Hardy-Rellich inequalities, we prove several Liouville theorems independently of the dimension N and on the sign of the solutions.
ENTIRE SOLUTIONS OF CERTAIN FOURTH ORDER ELLIPTIC PROBLEMS AND RELATED INEQUALITIES / Mitidieri, Enzo; D'Ambrosio, Lorenzo. - In: ADVANCES IN NONLINEAR ANALYSIS. - ISSN 2191-9496. - ELETTRONICO. - 11:1(2022), pp. 785-829. [10.1515/anona-2021-0217]
ENTIRE SOLUTIONS OF CERTAIN FOURTH ORDER ELLIPTIC PROBLEMS AND RELATED INEQUALITIES
MITIDIERI ENZO;
2022-01-01
Abstract
We study distributional solutions of semilinear biharmonic equations of the type ∆2u+f(u)=0 onRN, where f is a continuous function satisfying f(t)t ≥ c|t|q+1 for all t ∈ R with c > 0 and q > 1. By using a new approach mainly based on careful choice of suitable weighted test functions and a new version of Hardy-Rellich inequalities, we prove several Liouville theorems independently of the dimension N and on the sign of the solutions.| File | Dimensione | Formato | |
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