@article{Mawhin_Ruiz_2002, title={A strongly nonlinear Neumann problem at resonance with restrictions on the nonlinearity just in one direction}, volume={20}, url={https://apcz.umk.pl/TMNA/article/view/TMNA.2002.021}, abstractNote={Using topological degree techniques, we state and prove new sufficient
conditions for the existence of a solution of the Neumann boundary value
problem
$$
(|x’|^{p-2} x’)’ +f(t, x)+ h(t, x) =0,
\quad
x’(0) = x’(1)=0,
$$
when $h$ is bounded, $f$ satisfies a one-sided growth condition, $f + h$ some
sign condition, and the solutions of some associated homogeneous problem are
not oscillatory. A generalization of Lyapunov inequality is proved for a $p$-Laplacian equation. Similar results are given for the periodic problem.}, number={1}, journal={Topological Methods in Nonlinear Analysis}, author={Mawhin, Jean and Ruiz, David}, year={2002}, month={Sep.}, pages={1–14} }