A convex–concave problem with a nonlinear boundary condition

Journal of Differential Equations, no. 1 (2004): 91-128

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In this paper we study the existence of nontrivial solutions of the problem−Δu+u=|u|p−2uinΩ,∂u∂ν=λ|u|q−2uon∂Ω,with 1<q<2(N−1)/(N−2) and 1<p⩽2N/(N−2). In the concave–convex case, i.e., 1<q<2<p, if λ is small there exist two positive solutions while for λ large there is no positive solution. When p is critical, and q subcritical we obtain e...更多

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