The periodic Ambrosetti-Prodi problem for nonlinear perturbations of the p-Laplacian

• Autores: Jean Mawhin
• Localización: Journal of the European Mathematical Society, ISSN 1435-9855, Vol. 8, Nº 2, 2006, págs. 375-388
• Idioma: inglés
• DOI: 10.4171/jems/58
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• Resumen

  • We prove an Ambrosetti-Prodi-type result for the periodic solutions of equation $\left(|u'|^{p-2}u')\right)' + f(u)u' + g(x,u) = t ,$ when $f$ is arbitrary and $g(x,u) \to +\infty$ or $g(x,u)\to - \infty$ when $|u| \to \infty.$ The proof uses upper and lower solutions and Leray-Schauder degree.