In this paper we deal with singular boundary value problems of the type −div(a(x,u)∇u)+b(x)|∇u|2|u|θ sign (u)=f(x),u=0, in Ω, (0.1) on ∂Ω, where Ω is a open bounded set of RN with N>2 , a(x, t) is a Carathéodory function with polynomial growth with respect to t, b(x) is bounded and measurable, θ∈(0,1) and f(x) belongs to L1(Ω) . The main concern is to consider sign-changing solutions outside the energy space W1,20(Ω) .
Sign-changing solutions for elliptic problems with singular gradient terms and L1 data / Buccheri, Stefano. - In: NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS. - ISSN 1021-9722. - (2018).
Sign-changing solutions for elliptic problems with singular gradient terms and L1 data
Stefano Buccheri
2018
Abstract
In this paper we deal with singular boundary value problems of the type −div(a(x,u)∇u)+b(x)|∇u|2|u|θ sign (u)=f(x),u=0, in Ω, (0.1) on ∂Ω, where Ω is a open bounded set of RN with N>2 , a(x, t) is a Carathéodory function with polynomial growth with respect to t, b(x) is bounded and measurable, θ∈(0,1) and f(x) belongs to L1(Ω) . The main concern is to consider sign-changing solutions outside the energy space W1,20(Ω) .| File | Dimensione | Formato | |
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