Existence of multiple ordered solutions for a semilinear elliptic boundary value problem

Autor:	Melitta Fiebig-Wittmaack
Rok vydání:	1998
Předmět:	Elliptic operator Maximum principle Applied Mathematics Mathematical analysis Neumann boundary condition Free boundary problem Boundary value problem Mixed boundary condition Analysis Poincaré–Steklov operator Elliptic boundary value problem Mathematics
Zdroj:	Applicable Analysis. 70:61-66
ISSN:	1563-504X 0003-6811
DOI:	10.1080/00036819808840675
Popis:	We consider the problem of existence of multiple ordered solutions for the semi-linear elliptic boundary value problem where L is a second order uniformly elliptic operator. We show that for the case where f exhibits a certain type of oscillatory behavior and g is related to f by a boundedness condition, there exist multiple ordered solutions of the Neumann problem, related to the falling zeroes of the function f. Imposing a monotonicity condition on f we obtain inclusion results for the solutions of the problem, both in the autonomous case with general boundary conditions and in the nonautonomous Neumann case. The proof of our result is based on the maximum principle and on some theorems of Matano [7, 8]
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::68807bf0cc4ffcc3a75618ac4d0a7bfd https://doi.org/10.1080/00036819808840675 Zobrazit plný text záznamu