Lyapunov-type inequalities for quasilinear elliptic equations with Robin boundary condition
type: Item
instance of: scholarly article
title: Lyapunov-type inequalities for quasilinear elliptic equations with Robin boundary condition
zbMATH Open document ID: 1361.35059
author: Ülkü Dinlemez Kantar
author: Tülay Özden
published in: Journal of Inequalities and Applications
publication date: 2017-03-17T00:00:00Z
review text: The aim of this paper is to prove a Lyapunov-type inequality for the following two-dimensional quasilinear elliptic problem: \[ \begin{cases} -\big(\Phi_p(u_{xy}) \big)_y= r(x,y)\Phi_p(u), & (x,y)\in \Omega,\\ u(a_1,y)=0=u(b_1,y), & a_2\leq y\leq b_2,\\ u_x(x,a_2)=0=u_x(x,b_2), & a_1\leq x\leq b_1, \end{cases} \] where \(\Omega=[a_1,b_1]\times[a_2,b_2],\) \(r\) is a measurable function on \(\Omega,\) and \(\Phi_p(u)=|u|^{p-2}u.\) Also, a lower bound for the first positive eigenvalue of the boundary value problem is obtained.
Mathematics Subject Classification ID: 35J40
Mathematics Subject Classification ID: 35J66
Mathematics Subject Classification ID: 35J62
zbMATH DE Number: 6695881
zbMATH Keywords: two dimensional quasilinear elliptic problems
zbMATH Keywords: Lyapunov-type inequalities
Wikidata QID: Q42320929
reviewed by: Lubomira Softova
MaRDI profile type: Publication
full work available at URL: s13660-017-1320-4
OpenAlex ID: W2587840190
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DOI: 10.1186/S13660-017-1320-4
description: scientific article; zbMATH DE number 6695881