Boundary value problems for nonlinear perturbations of some ϕ-Laplacians

J. Mawhin

Banach Center Publications (2007)

  • Volume: 77, Issue: 1, page 201-214
  • ISSN: 0137-6934

Abstract

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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.

How to cite

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J. Mawhin. "Boundary value problems for nonlinear perturbations of some ϕ-Laplacians." Banach Center Publications 77.1 (2007): 201-214. <http://eudml.org/doc/281609>.

@article{J2007,
abstract = { 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. },
author = {J. Mawhin},
journal = {Banach Center Publications},
keywords = {Boundary value problem; mean curvature-like operator; Leray-Schauder degree},
language = {eng},
number = {1},
pages = {201-214},
title = {Boundary value problems for nonlinear perturbations of some ϕ-Laplacians},
url = {http://eudml.org/doc/281609},
volume = {77},
year = {2007},
}

TY - JOUR
AU - J. Mawhin
TI - Boundary value problems for nonlinear perturbations of some ϕ-Laplacians
JO - Banach Center Publications
PY - 2007
VL - 77
IS - 1
SP - 201
EP - 214
AB - 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.
LA - eng
KW - Boundary value problem; mean curvature-like operator; Leray-Schauder degree
UR - http://eudml.org/doc/281609
ER -

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