Bifurcation analysis of a singular nonlinear Sturm-Liouville equation
type: Item
instance of: scholarly article
zbMATH Open document ID: 1309.34030
DOI: 10.1142/S0219199714500126
author: Hernán Castro
published in: Communications in Contemporary Mathematics
publication date: 2014-10-15T00:00:00Z
Mathematics Subject Classification ID: 34B18
Mathematics Subject Classification ID: 34B16
Mathematics Subject Classification ID: 34B24
Mathematics Subject Classification ID: 34C23
zbMATH DE Number: 6356387
zbMATH Keywords: singular Sturm-Liouville equation
zbMATH Keywords: bifurcation analysis
zbMATH Keywords: positive solutions
MaRDI profile type: Publication
cites work: Emden-Fowler equations involving critical exponents
cites work: The Brézis-Nirenberg problem on \(\mathbb{S}^3\)
cites work: Best Sobolev constants and Emden equations for the critical exponent in \(S^3\)
cites work: Classification of the solutions of semilinear elliptic problems in a ball
cites work: The sharp constant in the Hardy-Sobolev-Maz'ya inequality in the three-dimensional upper half space
cites work: On some nonlinear Sturm-Liouville problems
cites work: Existence and bifurcation of solutions for an elliptic degenerate problem
cites work: A Relation Between Pointwise Convergence of Functions and Convergence of Functionals
cites work: Positive solutions of nonlinear elliptic equations involving critical sobolev exponents
cites work: Elliptic equations with critical exponent on spherical caps of \(S^{3}\)
cites work: Semilinear elliptic equations and supercritical growth
cites work: On the existence of extremal functions for a weighted Sobolev embedding with critical exponent
cites work: Critical point theory and the number of solutions of a nonlinear Dirichlet problem
cites work: A singular Sturm-Liouville equation under homogeneous boundary conditions
cites work: On the Caffarelli-Kohn-Nirenberg inequalities: sharp constants, existence (and nonexistence), and symmetry of extremal functions.
cites work: Some existence results for superlinear elliptic boundary value problems involving critical exponents
cites work: Bifurcation from simple eigenvalues
cites work: On pairs of positive solutions for a singular boundary value
cites work: Density, spectral theory and homoclinics for singular Sturm-Liouville systems
cites work: Maximum and anti-maximum principles for singular Sturm–Liouville problems
cites work: Nonlinear singular Sturm–Liouville problems
cites work: Existence of solutions for some nonlinear singular boundary value problems
cites work: Multiple solutions of semilinear elliptic problems in a ball
cites work: Symmetry and related properties via the maximum principle
cites work: On the Existence of Positive Solutions of Semilinear Elliptic Equations
cites work: Positive solutions of elliptic equations involving supercritical growth
cites work: Q4314556
cites work: On the infinitely many positive solutions of a supercritical elliptic problem
cites work: Q3027501
cites work: Some global results for nonlinear eigenvalue problems
cites work: Q4764973
cites work: Buckling of a heavy tapered rod.
cites work: Buckling of a critically tapered rod: global bifurcation
cites work: Buckling of a critically tapered rod: properties of some global branches of solutions
full work available at URL: s0219199714500126
OpenAlex ID: W2106893494
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title: Bifurcation analysis of a singular nonlinear Sturm-Liouville equation
review text: A voluminous work about the existence of positive solutions for the singular Sturm-Liouville problem NEWLINE\[NEWLINE-(x^{2\alpha}u')' = \lambda u+u^{p}, u>0, u(1) = 0.NEWLINE\]NEWLINE Contrary to other works, the proofs do not rely on the change of variables. The author works directly with the equation.
reviewed by: Erdoǧan Şen
description: scientific article; zbMATH DE number 6356387