Jumping nonlinearities for fourth order B.V.P.

Marta García-Huidobro; Raúl Manásevich

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Existence and non-existence of sign-changing solutions for a class of two-point boundary value problems involving one-dimensional $p$ -Laplacian

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We consider the boundary value problem involving the one dimensional $p$ -Laplacian, and establish the precise intervals of the parameter for the existence and non-existence of solutions with prescribed numbers of zeros. Our argument is based on the shooting method together with the qualitative theory for half-linear differential equations.