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.