A strongly nonlinear Neumann problem at resonance with restrictions on the nonlinearity just in one direction
Keywords
Neuman problem, periodic solutions, p-Laplacian equation, topological degree, Lyapunov inequalityAbstract
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.Downloads
Published
2002-09-01
How to Cite
1.
MAWHIN, Jean and RUIZ, David. A strongly nonlinear Neumann problem at resonance with restrictions on the nonlinearity just in one direction. Topological Methods in Nonlinear Analysis. Online. 1 September 2002. Vol. 20, no. 1, pp. 1 - 14. [Accessed 25 April 2024].
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