Boundary Value Problem for One-Dimensional Elliptic Jumping Problem with Crossing $n-$eigenvalues
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Thispaperisdealtwithone-dimensionalellipticjumpingprob- lem with nonlinearities crossing n eigenvalues. We get one theorem which shows multiplicity results for solutions of one-dimensional elliptic bound- ary value problem with jumping nonlinearities. This theorem is that there exist at least two solutions when nonlinearities crossing odd eigenvalues, at least three solutions when nonlinearities crossing even eigenvalues, exactly one solutions and no solution depending on the source term. We obtain these results by the eigenvalues and the corresponding normalized eigen- functions of the elliptic eigenvalue problem and Leray-Schauder degree theory.
Abstract
Thispaperisdealtwithone-dimensionalellipticjumpingprob- lem with nonlinearities crossing n eigenvalues. We get one theorem which shows multiplicity results for solutions of one-dimensional elliptic bound- ary value problem with jumping nonlinearities. This theorem is that there exist at least two solutions when nonlinearities crossing odd eigenvalues, at least three solutions when nonlinearities crossing even eigenvalues, exactly one solutions and no solution depending on the source term. We obtain these results by the eigenvalues and the corresponding normalized eigen- functions of the elliptic eigenvalue problem and Leray-Schauder degree theory.
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