Electron. J. Diff. Equ., Vol. 2014 (2014), No. 30, pp. 1-10.

Exact number of solutions for a Neumann problem involving the p-Laplacian

Justino Sanchez, Vicente Vergara

We study the exact number of solutions of the quasilinear Neumann boundary-value problem
 (\varphi_p(u'(t)))'+g(u(t))=h(t)\quad\text{in } (a,b),\cr
where $\varphi_p(s)=|s|^{p-2}s$ denotes the one-dimensional p-Laplacian. Under appropriate hypotheses on g and h, we obtain existence, multiplicity, exactness and non existence results. The existence of solutions is proved using the method of upper and lower solutions.

Submitted September 26, 2013. Published January 27, 2014.
Math Subject Classifications: 34B15, 35J60.
Key Words: Neumann boundary value problem; p-Laplacian; lower-upper solutions; exact multiplicity.

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Justino Sánchez
Departamento de Matemáticas, Universidad de La Serena
Avda. Cisternas 1200, La Serena, Chile
email: jsanchez@userena.cl
Vicente Vergara
Instituto de Alta Investigación, Universidad de Tarapacá
Antofagasta No. 1520, Arica, Chile
email: vvergaraa@uta.cl

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