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

  • Jean Mawhin

    Université Catholique de Louvain, Belgium

Abstract

We prove an Ambrosetti-Prodi-type result for the periodic solutions of equation (up2u))+f(u)u+g(x,u)=t,\left(|u'|^{p-2}u')\right)' + f(u)u' + g(x,u) = t , when ff is arbitrary and g(x,u)+g(x,u) \to +\infty or g(x,u)g(x,u)\to - \infty when u.|u| \to \infty. The proof uses upper and lower solutions and Leray-Schauder degree.

Cite this article

Jean Mawhin, The periodic Ambrosetti-Prodi problem for nonlinear perturbations of the p-Laplacian. J. Eur. Math. Soc. 8 (2006), no. 2, pp. 375–388

DOI 10.4171/JEMS/58