TY - JOUR
AU - Mawhin, Jean
AU - Ruiz, David
PY - 2002/09/01
Y2 - 2023/03/29
TI - A strongly nonlinear Neumann problem at resonance with restrictions on the nonlinearity just in one direction
JF - Topological Methods in Nonlinear Analysis
JA - TMNA
VL - 20
IS - 1
SE -
DO -
UR - https://apcz.umk.pl/TMNA/article/view/TMNA.2002.021
SP - 1 - 14
AB - Using topological degree techniques, we state and prove new sufficientconditions for the existence of a solution of the Neumann boundary valueproblem$$(|x'|^{p-2} x')' +f(t, x)+ h(t, x) =0,\quadx'(0) = x'(1)=0,$$when $h$ is bounded, $f$ satisfies a one-sided growth condition, $f + h$ somesign condition, and the solutions of some associated homogeneous problem arenot oscillatory. A generalization of Lyapunov inequality is proved for a $p$-Laplacian equation. Similar results are given for the periodic problem.
ER -