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In this paper we study a nonlinear boundary eigenvalue problema governed by the one-dimensional p-Laplacian operator with impulse, we give some properties of the first eigenvalue λ1 and we prove the existence of eigenvalues sequence {λn}n∈N∗ by using the Lusternik-Schnirelman principle, as well as by the characterization of the sequence of eigenvalues, we discuss the strict monotonicity of the first eigenvalue and we prove that the eigenfunction corresponding to second eigenvalue λ2 changes sign only once on [0, 1].

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