Please use this identifier to cite or link to this item: http://hdl.handle.net/10773/18732
Title: Existence Results for Quasilinear Elliptic Equations with Multivalued Nonlinear Terms
Author: Otani, Mitsuharu
Staicu, Vasile
Keywords: Strong solutions Quasilinear elliptic equations Multivalued pertur Subdifferential operator
Issue Date: 2014
Publisher: Springer
Abstract: In this paper we study the existence of solutions u ∈ W1,p0(Ω) with △pu ∈ L2(Ω) for the Dirichlet problem {−△pu(x)∈−∂Φ(u(x))+G(x,u(x)),x∈Ω,u∣∂Ω=0, (1) where Ω ⊆ RN is a bounded open set with boundary ∂Ω, △p stands for the p−Laplace differential operator, ∂Φ denotes the subdifferential (in the sense of convex analysis) of a proper convex and lower semicontinuous function Φ and G : Ω × R → 2R is a multivalued map. We prove two existence results: the first one deals with the case where the multivalued map u ↦ G(x, u) is upper semicontinuous with closed convex values and the second one deals with the case when u ↦ G(x, u) is lower semicontinuous with closed (not necessarily convex) values.
Peer review: yes
URI: http://hdl.handle.net/10773/18732
DOI: 10.1007/s11228-014-0289-0
ISSN: 1877-0541
Appears in Collections:CIDMA - Artigos
FAAG - Artigos

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