Remarks on an elliptic equation of Kirchhoff type

By To Fu Ma. 2005

222 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/fb9df3b9a45b3eb477dca87e0ded586a68b7704e

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In Applied Mathematics

In Computational Theory and Mathematics

In Control and Systems Engineering

Citations in the corpus

Multiplicity of solutions for p ( x ) -polyharmonic elliptic Kirchhoff equations (2011, methodology): “The existence of positive solutions of non-degenerate Kirchhoff-type problems is treated in [7–9] for L = 1.”
Multiplicity and concentration behavior of positive solutions for a Schrödinger–Kirchhoff type problem via penalization method (2013, background): “The reader may consult [1], [2], [3], [9], [10], [14], [21] and the references therein, for more informations on nonlocal problems.”
Multiplicity results for a class of $p(x)$-Kirchhoff type equations with combined nonlinearities (2012, background): “In recent years, elliptic problems involving p-Kirchhoff type operators have been studied in many papers, we refer to [2, 3, 4, 17, 18, 21, 22], in which the authors have used different methods to get the existence of solutions for (1.”
ON A CLASS OF NONLOCAL ELLIPTIC PROBLEMS WITH CRITICAL GROWTH (2010, background): “We have to point out that nonlocal problems also appear in other fields as, for example, biological systems where u describes a process which depends on the average of itself (for example, population density).”
Existence of a nodal solution with minimal energy for a Kirchhoff equation (2015, background): “Therefore, the study on this class of problems has increased considerably in the last ten years, as can be seen in [1], [2], [6], [10], [12]–[17], [19], [20]–[22], [26]–[29] and references therein.”
Existence of solution for a class of nonlocal elliptic problem via sub-supersolution method (2013, background): “More details about this class of problem can be see in [4], [5], [7], [16], [20] and [21] and their references.”
Study of a nonlinear Kirchhoff equation with non-homogeneous material (2014, methodology): “[19], [27], [28] and [29] using genus or category theory.”
Infinitely many solutions for a fractional Kirchhoff type problem via Fountain Theorem (2015, background): “where Ω ⊂ R is a smooth domain, u satisfies some boundary conditions, see for example [1,13,14,24] for more information about Eq.”
Existence and Concentration Result for the Kirchhoff Type Equations with General Nonlinearities (2014, background): “For instance, we refer to [3,4,30,31,50,53] and references therein.”