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

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.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11367/18610
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