[tel-00011384, v1] Méthodes d'analyse non linéaire dans l'étude des problèmes aux limites

Methods in the NonlinearAnalysis for the Study ofBoundary Value Problems‚ ‚^Metode de analiza neliniara ‡n studiul‚problemelor la limitaPh.D. Thesis defended by‚Teodora{Liliana Radulescuat the Babes»{Bolyai University, Cluj{Napoca, 2005Adviser: Prof. Dr. Radu Precuptel-00011384, version 1 - 15 Jan 2006ContentsIntroduction 31 Entire solutions of nonlinear eigenvalue problems 201.1 A class of nonlinear eigenvalue logistic with sign-changing potential and absorption . . . . . . . . . . . . . . . . 201.2 Proof of Theorem 1 . . . . . . . . . . . . . . . . . . . . . . . . . 241.3 An auxiliary result . . . . . . . . . . . . . . . . . . . . . . . . . 261.4 Proof of Theorem 2 . . . . . . . . . . . . . . . . . . . . . . . . . 282 Entire solutions of nonlinear elliptic equations 352.1 Entire solutions of sublinear elliptic in anisotropicmedia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362.2 Proof of Theorem 3 . . . . . . . . . . . . . . . . . . . . . . . . . 382.3 Proof of 4 . . . . . . . . . . . . . . . . . . . . . . . . . 432.3.1 Existence . . . . . . . . . . . . . . . . . . . . . . . . . . 432.3.2 Uniqueness . . . . . . . . . . . . . . . . . . . . . . . . . 452.4 EntirepositivesolutionsofthesingularEmden-Fowlerequationwith nonlinear gradient term . . . . . . . . . . . . . . . . . . . 473 Semilinear elliptic problems with sign-changing potential andsubcritical nonlinearity 523.1 ...