Electronic Journal of Differential Equations,
Vol. 2014 (2014), No. 30, pp. 1-10.

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

Authors: Justino Sanchez (Univ. de La Serena, Chile)
         Vicente Vergara (Univ. de Tarapaca, Arica, Chile)
 
Abstract:
 We study the exact number of solutions of the quasilinear Neumann
 boundary-value problem
 $$\displaylines{
 (\varphi_p(u'(t)))'+g(u(t))=h(t)\quad\text{in } (a,b),\cr
 u'(a)=u'(b)=0,
 }$$
 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.