Global bifurcation, Berestyckias conjecture and one-sign solutions for pp-Laplacian

In this paper, we shall establish the unilateral global bifurcation result from an interval for a class of high-dimensional pp-Laplacian problems. As an application of the above result, we shall prove the existence of the principal half-eigenvalues for a class of half-quasilinear eigenvalue problems...

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Bibliographic Details
Published inNonlinear analysis Vol. 91; pp. 51 - 59
Main Authors Dai, Guowei, Ma, Ruyun
Format Journal Article
LanguageEnglish
Published 01.11.2013
Subjects
Bifurcations
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Summary:In this paper, we shall establish the unilateral global bifurcation result from an interval for a class of high-dimensional pp-Laplacian problems. As an application of the above result, we shall prove the existence of the principal half-eigenvalues for a class of half-quasilinear eigenvalue problems. Our result partially answers the open problem proposed by Berestycki. Moreover, we shall investigate the existence of one-sign solutions for a class of high-dimensional pp-Laplacian problems with non-papa1-homogeneous nonlinearities.
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ISSN:0362-546X
DOI:10.1016/j.na.2013.06.003