|
|||||
|
|
Elliptic equations with vertical asymptotes in the nonlinear term |
|
| Authors: | Louis Dupaigne Augusto C Ponce Alessio Porretta |
| Institution: | 1. Laboratoire Amiénois de Mathématique Fondamentale et Appliquée Faculté de Mathématiques et d'Informatique, Université Picardie Jules Verne, 33, rue Saint-Leu, 80039, Amiens Cedex 1, France 2. Laboratoire de Mathématiques et Physique Théorique Fédération Denis Poisson, Université Fran?ois Rabelais, 37200, Tours, France 3. Dipartmento di Matematica, Università di Roma “Tor Vergata”, Via della Ricerca Scientifica 1, 00133, Roma, Italy |
| Abstract: | We study the existence of solutions of the nonlinear problem {fx349-1} where μ is a bounded measure andg is a continuous nondecreasing function such thatg(0)=0. In this paper, we assume that the nonlinearityg satisfies {fx349-2} Problem (0.1) need not have a solution for every measure μ. We prove that, given μ, there exists a “closest” measure μ* for which (0.1) can be solved. We also explain how assumption (0.2) makes problem (0.1) different from the case whereg(t) is defined for everyt ∈ ℝ. |
| Keywords: | |
| 本文献已被 SpringerLink 等数据库收录！ | |