Existence of Multiple Solutions of a Two-point Boundary Value Problem at Resonance
نویسندگان
چکیده
(1.1) { − ·· u= nu+ g(t, u), t ∈ (0, π), u(0) = u(π) = 0, where n ∈ N and g : [0, π] × R → R is a continuously differentiable function satisfying the following assumptions: (g1) g(t, 0) ≡ 0. (g2) lim|s|→∞ g′ s(t, s) = 0 uniformly in t ∈ (0, π). (g3) There exists R0 > 0 such that g(t, s)s > 0 for any s ∈ R with |s| ≥ R0 and for a.e. t ∈ (0, π). (g4) There exist some positive numbers C1, C2, R1 and r with 0 < r < 1 such that
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