Electronic Journal of Differential Equations,
Vol. 2005(2005), No. 08, pp. 1-10.

Title: Strong resonance problems for the one-dimensional p-Laplacian

Author: Jiri Bouchala (Univ. Ostrava, Czech republic)

Abstract: 
   We study the existence of the weak solution of the
   nonlinear boundary-value problem
   $$\displaylines{
   -(|u'|^{p-2}u')'= \lambda  |u|^{p-2}u + g(u)-h(x)\quad 
   \hbox{in  }  (0,\pi) ,\cr
   u(0)=u(\pi )=0\,,
   }$$
   where $p$ and $\lambda$ are real numbers, $p>1$,
   $h\in L^{p'}(0,\pi )$ ($p' =\frac{p}{p-1}$) and the nonlinearity
   $g:\mathbb{R} \to \mathbb{R}$ is a continuous function of the
   Landesman-Lazer type.    Our sufficiency conditions generalize the
   results published previously  about the solvability of this problem.

Submitted June 21, 2004. Published January 5, 2005.
Math Subject Classifications: 34B15, 34L30, 47J30.
Key Words: p-Laplacian; resonance at the eigenvalues; 
           Landesman-Lazer  type conditions.