Positive solutions for singular superlinear \(\phi\)-Laplacian problems with nonlinear boundary conditions
type: Item
instance of: scholarly article
title: Positive solutions for singular superlinear \(\phi\)-Laplacian problems with nonlinear boundary conditions
zbMATH Open document ID: 1494.34086
author: D. D. Hai
author: X. Wang
published in: Mediterranean Journal of Mathematics
publication date: 2022-01-27T00:00:00Z
review text: The paper deals with positive solutions of the boundary value problem \[ \begin{cases} -(\phi(u'))' = \lambda h(t) f(u), \\ u(0)=0, \quad u'(1)+H(u(1))=0, \end{cases} \] where \(\lambda>0\) is a parameter, \(\phi\colon\mathbb{R}\to\mathbb{R}\) is an odd increasing homeomorphism, \(h \colon (0,1]\to (0,+\infty)\) is continuous, \(f \colon (0,+\infty)\to (0,+\infty)\) is continuously differentiable with \(\inf f>0\), and \(\phi\)-superlinear at \(+\infty\), with possible singularity at \(0\), \(H\colon [0,+\infty)\to [0,+\infty)\) is continuous, nondecreasing, with \(H(0)=0\). Using the fixed point theory and the topological degree, the authors prove the existence of \(\lambda^{*}>0\) such that there are at least two (ordered) solutions for \(\lambda<\lambda^{*}\), at least one solution for \(\lambda=\lambda^{*}\), and no solution for \(\lambda>\lambda^{*}\).
reviewed by: Guglielmo Feltrin
Mathematics Subject Classification ID: 34B09
Mathematics Subject Classification ID: 34B08
Mathematics Subject Classification ID: 34B18
Mathematics Subject Classification ID: 34B16
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 7465533
zbMATH Keywords: nonlinear boundary conditions
zbMATH Keywords: \(\phi\)-Laplacian
zbMATH Keywords: positive solutions
zbMATH Keywords: topological degree
zbMATH Keywords: Schauder fixed point theorem
MaRDI profile type: Publication
full work available at URL: s00009-021-01963-7
OpenAlex ID: W4210244764
cites work: On the number of solutions of asymptotically superlinear two point boundary value problems
cites work: Combined effects of concave and convex nonlinearities in some elliptic problems
cites work: Pairs of positive solutions for the one-dimensional p-Laplacian
cites work: Multiplicity and uniqueness of positive solutions for elliptic equations with nonlinear boundary conditions arising in a theory of thermal explosion
cites work: Q4871247
cites work: On the number of positive radial solutions for singular superlinear problems in the exterior of a ball
cites work: Q5617863
cites work: Positive radial solutions and non-radial bifurcation for semilinear elliptic equations in annular domains
cites work: On the Existence of Positive Solutions of Semilinear Elliptic Equations
DOI: 10.1007/S00009-021-01963-7
Recommended article: Existence and multiplicity of positive solutions for singular $\phi$-Laplacian superlinear problems with nonlinear boundary conditions
Recommended article: Positive solutions to superlinear singular boundary value problems
Recommended article: Positive solutions for nonlinear singular superlinear elliptic equations
Recommended article: Positive solutions of superlinear semipositone singular Dirichlet boundary value problems
Recommended article: Q4542743
Recommended article: Positive solutions for a singular and superlinear \(p\)-Laplacian problem with gradient term
Recommended article: Q5428536
Recommended article: Exact structure of positive solutions for a \(p\)-Laplacian problem involving singular and superlinear nonlinearities
Recommended article: Existence of positive solutions for \(n\)th-order \(p\)-Laplacian singular super-linear boundary value problems
Recommended article: Q4514304
description: scientific article; zbMATH DE number 7465533