We prove the uniqueness of the weak solution of noncoercive nonlinear elliptic problems whose model is u ∈ W_^1,p (Ω), -div(a(x)(1+|∇u|^2)^(p-2)/2 ∇u)+b(x)(1+|∇u|2)(σ+1)/2=f in D′(Ω), where Ω is a bounded open subset of RN, N>2, p satisfies p ≥2N/(N+1), a is a function belonging to L^∞(Ω) such that a(x) ≥α>0, f belongs to the dual space W-1,p′(Ω), b belongs to some Lebesgue space L^r(Ω) with r>r*(N,p) and σ belongs to the interval [0,σ*(N,p,r)], with σ*(N,p,r) and r*(N,p) functions which are specified below.

Uniqueness results for nonlinear elliptic equations with a lower order term

Betta, MF;
2005-01-01

Abstract

We prove the uniqueness of the weak solution of noncoercive nonlinear elliptic problems whose model is u ∈ W_^1,p (Ω), -div(a(x)(1+|∇u|^2)^(p-2)/2 ∇u)+b(x)(1+|∇u|2)(σ+1)/2=f in D′(Ω), where Ω is a bounded open subset of RN, N>2, p satisfies p ≥2N/(N+1), a is a function belonging to L^∞(Ω) such that a(x) ≥α>0, f belongs to the dual space W-1,p′(Ω), b belongs to some Lebesgue space L^r(Ω) with r>r*(N,p) and σ belongs to the interval [0,σ*(N,p,r)], with σ*(N,p,r) and r*(N,p) functions which are specified below.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11367/18610
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 29
  • ???jsp.display-item.citation.isi??? 25
social impact