Boundary value problems for nonlinear perturbations of some ϕ-Laplacians

• Autorzy: J. Mawhin
• Języki publikacji: EN

Abstrakty

EN

This paper surveys a number of recent results obtained by C. Bereanu and the author in existence results for second order differential equations of the form
(ϕ(u'))' = f(t,u,u')
submitted to various boundary conditions. In the equation, ϕ: ℝ → ≤ ]-a,a[ is a homeomorphism such that ϕ(0) = 0. An important motivation is the case of the curvature operator, where ϕ(s) = s/√(1+s²). The problems are reduced to fixed point problems in suitable function space, to which Leray-Schauder theory is applied.

Kategorie tematyczne

• 34B15: Nonlinear boundary value problems
• 47H10: Fixed-point theorems

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2007
• Tom: 77
• Numer: 1
• Strony: 201-214

Daty

wydano

2007

Twórcy

autor

J. Mawhin

• Université Catholique de Louvain, Département de mathématique, Chemin du Cyclotron, 2, B-1348 Louvain-la-Neuve, Belgique

Identyfikatory

DOI

10.4064/bc77-0-15