MR2976040 Sophia Th. KYRITSI and Nikolaos S. PAPAGEORGIOU Sophia Th. KYRITSI and Nikolaos S. PAPAGEORGIOU A Bifurcation-Type Result for Nonlinear Neumann Eigenvalue Problems Funkcialaj Ekvacioj. Serio Internacia 55 2012 1--15 http://fe.math.kobe-u.ac.jp/FE/FullPapers/55-1/55_1.pdf http://www.ams.org/mathscinet-getitem?mr=MR2976040 We consider a nonlinear Neumann eigenvalue problem driven by the $p$-Laplacian and with a $(p-1)$-sublinear reaction. Using variational methods together with suitable truncation techniques, we prove a bifurcation-type theorem for the eigenvalue problem. Namely, we show that there is a critical parameter value $\lambda_*>0$ such that for all $\lambda>\lambda_*$ the problem has at least two positive solutions, for $\lambda=\lambda_*$ there is at least one positive solution and for $\lambda\in(0,\lambda_*)$ no positive solutions exist. $p$-Laplacian, Nonlinear maximum principle, Local minimizers, Nonlinear regularity, Bifurcation-type theorem, Positive solution. 35J20, 35J60, 35J92. 55-1 2012 A Bifurcation-Type Result for Nonlinear Neumann Eigenvalue Problems Sophia Th. KYRITSI and Nikolaos S. PAPAGEORGIOU Sophia Th. KYRITSI and Nikolaos S. PAPAGEORGIOU
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