The authors consider the impulsive differential equation with Monge-Ampère operator in the form of ⎧ ⎪⎨ ⎪⎩ ((u (t))n) = λntn–1f(–u(t)), t ∈ (0, 1),t = tk, k = 1, 2, ... ,m, (u ) n|t=tk = λIk(–u(tk)), k = 1, 2, ... ,m, u (0) = 0, u(1) = 0, where λ is a nonnegative parameter and n ≥ 1. We show the existence, uniqueness, and continuity results. Our approach is largely based on the eigenvalue theory and the theory of α-concave operators. The nonexistence result of a nontrivial convex solution is also studied by taking advantage of the internal geometric properties related to the problem.

EB00000003708K

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