Multiple Positive Solutions of Semilinear Differential Equations with Singularities

By Kunquan Lan. 2001

227 citations recorded by the source corpus.

Subfields: Applied Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/0bf6d376b401910efe3c68ec299c83498afe1ca8

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In Applied Mathematics

In Numerical Analysis

Citations in the corpus

Non-negative solutions of systems of ODEs with coupled boundary conditions (2012, background): “We stress that, by expanding the lists in conditions ðS5Þ; ðS6Þ below, it is possible to state results for four or more positive solutions, see for example the paper by Lan [21] for the type of results that might be stated.”
Solutions of perturbed Hammerstein integral equations with applications (2016, result): “[58] K. Q. Lan and W. Lin, Positive solutions of systems of singular Hammerstein integral equations with applications to semilinear elliptic equations in annuli, Nonlinear Anal., 74 (2011), 7184–7197.”
Positive Solutions of Nonlocal Boundary Value Problems: A Unified Approach (2006, methodology): “The set Vρ was essentially introduced in [12], in fact Vρ = Ωρ/c using the notation of [12].”
Non‐local boundary value problems of arbitrary order (2009, methodology): “These lemmas are essentially well known; see, for example, [20, 34].”
Loss of positivity in a nonlinear scalar heat equation (2006, methodology): “We do not do state such results leaving them to the reader who may refer to [ 9 ] for the type of result that may be stated.”
Multiple nonnegative solutions of systems with coupled nonlinear boundary conditions (2013, unknown): “Ωρ/c is an extension to the case of systems of a set given by Lan [31].”
NONLINEAR NON-LOCAL BOUNDARY-VALUE PROBLEMS AND PERTURBED HAMMERSTEIN INTEGRAL EQUATIONS (2006, background): “We leave these to the reader, who may consult [13] to see the type of result that may be stated.”
Positive solutions of nonlocal boundary value problems involving integral conditions (2008, methodology): “The set Vρ was essentially introduced in [10], in fact Vρ = Ωρ/c using the notation of [10].”
Nonzero radial solutions for a class of elliptic systems with nonlocal BCs on annular domains (2014, unknown): “Ω is an extension to the case of systems of a set given by Lan [33].”