On the eigencurves of one dimensional p-Laplacian with weights for an elliptic Neumann problem

  • Ahmed SanhajiEmail author
  • Ahmed Dakkak


In the present paper we study the existence of the eigencurves of one dimensional p-Laplacian with indefinite weights of the Neumann problem for the following elliptic equation
$$\begin{aligned} \left\{ \begin{array}{ll} -\left( |u'|^{p-2}u'\right) ' =\left( \alpha \, m_{1}(x)+\beta \,m_{2}(x)\right) |u|^{p-2}u\quad \text{ in } \; I = {]a,b[}\\ \quad \\ u'(a)=u'(b) = 0. \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \end{array} \right. \end{aligned}$$
Moreover, we establish their variational formulations and asymptotic behavior. Finally, we prove some properties of the principal eigencurve such as concavity and differentiability.


p-Laplacian Eigencurves One dimensional 

Mathematics Subject Classification

35J30 35J60 35J66 



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© Springer-Verlag Italia S.r.l., part of Springer Nature 2019

Authors and Affiliations

  1. 1.Laboratory LSI Department of Mathematics, Polydisciplinary, Faculty of TAZAUniversity Sidi Mohamed Ben AbdellahTAZAMorocco

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