Korean J. Math. Vol. 26 No. 4 (2018) pp.683-700
DOI: https://doi.org/10.11568/kjm.2018.26.4.683

One-dimensional jumping problem involving $p$-Laplacian

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Published: Dec 30, 2018
Keywords:
One-dimensional p-Laplacian problem, one-dimensional pU00100000Laplacian eigenvalue problem, jumping nonlinearity, Leray-Schauder degree theory.
Mathematics Subject Classification:
one-dimensional pô€€€Laplacian eigenvalue problem, 35A01, 35A16, 35J30, 35J40,

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Tacksun Jung
Department of Mathematics, Kunsan National University, Kunsan 573-701, Korea
Q-Heung Choi
Department of Mathematics Education Inha University Incheon 402-751, Korea

Abstract

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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Supporting Agencies

Basic Science Research Program through the Na- tional Research Foundation of Korea(NRF) funded by the Ministry of Science

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