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We get one theorem which shows existence of solutions for one-dimensional jumping problem involving $p$-Laplacian and Dirichlet boundary condition. This theorem is that there exists at least one solution when nonlinearities crossing finite number of eigenvalues, exactly one solutions and no solution depending on the source term. We obtain these results by the eigenvalues and the corresponding normalized eigenfunctions of the $p-$Laplacian eigenvalue problem when $1<p<\infty$, variational reduction method and Leray-Schauder degree theory when $2\le p<\infty$.
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