Existence of a positive solution for one-dimensional singular \(p\)-Laplacian problems and its parameter dependence
type: Item
instance of: scholarly article
title: Existence of a positive solution for one-dimensional singular \(p\)-Laplacian problems and its parameter dependence
zbMATH Open document ID: 1316.34029
author: Xuemei Zhang
author: Meiqiang Feng
published in: Journal of Mathematical Analysis and Applications
publication date: 2015-03-27T00:00:00Z
review text: The authors consider consider one-dimensional singular \(p\)-Laplacian problem \[ \lambda (\varphi_p(u'))'+w(t)f(t,u) = 0, \] \[ au(0)- bu'(0) =\int^1_0 g(t)u(t)dt, u'(1) = 0, \] where \(\lambda\) is a positive parameter, \(p(s) = |s|^{p-2}s\), \(p > 1\), and \(w\) may be singular at \(t = 0\) and/or \(t = 1\). Using fixed-point techniques, they establish some existence, multiplicity, and nonexistence results. They also study the dependence of the positive solution \(u_\lambda(t)\) on the parameter \(\lambda\).
Mathematics Subject Classification ID: 34B18
Mathematics Subject Classification ID: 34B16
Mathematics Subject Classification ID: 47N20
Mathematics Subject Classification ID: 34B08
zbMATH DE Number: 6420280
zbMATH Keywords: positive solutions
zbMATH Keywords: p-Laplacian
zbMATH Keywords: cone
reviewed by: Ruyun Ma
MaRDI profile type: Publication
full work available at URL: j.jmaa.2013.11.038
OpenAlex ID: W2067045209
cites work: Eigenvalues and the one-dimensional \(p\)-Laplacian
cites work: Steady-state turbulent flow with reaction
cites work: Multiplicity theorems for the Dirichlet problem involving the \(p\)-Laplacian.
cites work: Extremal solutions for nonlinear functional \(\varphi\)-Laplacian impulsive equations
cites work: Unilateral global bifurcation phenomena and nodal solutions for \(p\)-Laplacian
cites work: Bifurcation from infinity and nodal solutions of quasilinear problems without the signum condition
cites work: Eigenvalues, bifurcation and one-sign solutions for the periodic \(p\)-Laplacian
cites work: A multiplicity result for \(p\)-Lapacian boundary value problems via critical points theorem
cites work: Approximation of a nonlinear elliptic problem arising in a non-Newtonian fluid flow model in glaciology
cites work: Existence, multiplicity, and dependence on a parameter for a periodic boundary value problem
cites work: Q3994493
cites work: On discrete fourth-order boundary value problems with three parameters
cites work: Nonlinear eigenvalue problems for quasilinear systems
cites work: Exact number of solutions of stationary reaction-diffusion equations
cites work: The existence of symmetric positive solutions for Sturm-Liouville-like four-point boundary value problem with a \(p\)-laplacian operator
cites work: Bifurcation of sign-changing solutions for one-dimensional \(p\)-Laplacian with a strong singular weight; \(p\)-sublinear at \(\infty \)
cites work: Bifurcation of sign-changing solutions for one-dimensional \(p\)-Laplacian with a strong singular weight: \(p\)-superlinear at \(\infty \)
cites work: Second order singular boundary value problems with integral boundary conditions
cites work: Eigenvalue problems for second-order nonlinear dynamic equations on time scales
cites work: Existence and uniqueness of positive periodic solutions of functional differential equations
cites work: Multiple positive solutions for the one-dimensional singular \(p\)-Laplacian.
cites work: Existence and iteration of monotone positive solutions for multipoint boundary value problem with \(p\)-Laplacian operator
cites work: Multiple positive solutions of singular eigenvalue type problems involving the one-dimensional \(p\)-Laplacian
cites work: On the number of positive solutions of nonlinear systems.
cites work: Positive solutions of a focal problem for one-dimensional \(p\)-Laplacian equations
cites work: Impulsive boundary value problems involving the one-dimensional \(p\)-Laplacian
DOI: 10.1016/J.JMAA.2013.11.038
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description: scientific article; zbMATH DE number 6420280