We study distributional solutions of semilinear biharmonic equations of the type Δ2u+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
D’Ambrosio, Lorenzo;
2022-01-01
Abstract
We study distributional solutions of semilinear biharmonic equations of the type Δ2u+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 in questo prodotto:
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