African Diaspora Journal of Mathematics

Existence of Solutions of Some Nonlinear $φ$-Laplacian Equations with Neumann-Steklov Nonlinear Boundary Conditions

Charles Etienne Goli and Assohoun Adje

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

We study the existence of solutions of the quasilinear equation $$(D(u(t))\phi(u'(t)))'=f(t,u(t),u'(t)),\qquad a.e. \;\;t\in [0,T],$$ subject to nonlinear Neumann-Steklov boundary conditions on $[0,T]$, where $\phi: (-a,a)\rightarrow \mathbb{R}$ (for $0 < a < \infty$) is an increasing homeomorphism such that $\phi(0)=0$, $f:[0,T]\times\mathbb{R}^{2} \rightarrow \mathbb{R}$ a $L^1$-Carathéodory function, $D$ : $\mathbb{R}\longrightarrow (0,\infty)$ is a continuous function. Using topological methods, we obtain existence and multiplicity results.

Article information

Source
Afr. Diaspora J. Math. (N.S.), Volume 20, Number 2 (2017), 16-38.

Dates
First available in Project Euclid: 17 May 2017

Permanent link to this document
https://projecteuclid.org/euclid.adjm/1494986433

Mathematical Reviews number (MathSciNet)
MR3637473

Zentralblatt MATH identifier
1370.34041

Subjects
Primary: 34B15: Nonlinear boundary value problems

Keywords
$ϕ$−Laplacian $L^1$-Carathéodory function Nonlinear Neumann-Steklov problem Leray-Schauder degree Brouwer degree lower and upper-solutions

Citation

Goli, Charles Etienne; Adje, Assohoun. Existence of Solutions of Some Nonlinear $φ$-Laplacian Equations with Neumann-Steklov Nonlinear Boundary Conditions. Afr. Diaspora J. Math. (N.S.) 20 (2017), no. 2, 16--38. https://projecteuclid.org/euclid.adjm/1494986433


Export citation