Time: 9h30, Tuesday, November 3, 2015
Location: Room 4, Building A14, Institute of Mathematics, 18 Hoang Quoc Viet, Cau Giay, Hanoi
Abstract: We prove the existence of weak solutions of Neumann problem for a nonuniformly semilinear elliptic equation:
{−div(h(x)∇u)+a(x)u=λθ(x)u+f(x,u)−k(x)∂u∂n=g(x,u) in Ω on ∂Ω, where Ω⊂R^N, N≥3 is an unbounded domain with smooth and bounded boundary ∂Ω, Ω¯=Ω∪∂Ω, h(x)∈L_{1loc}(Ω¯), a(x)∈C(Ω¯), a(x)→+∞ as |x|→+∞, f(x,s), x∈Ω, g(x,s), x∈∂Ω are Carathéodory, k(x)∈L_2(Ω), θ(x)∈L∞(Ω¯), θ(x)≥0.
Our arguments is based on the minimum principle and rely essentially on a generalization of the Landesman-Lazer type condition.