Sign changing solutions of Kirchhoff type problems via invariant sets of descent flow

By Zhitao Zhang, Kanishka Perera. 2006

444 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/adaa6da1fd79258518ef4bb2060b889d3ba0b61b

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Infinitely many solutions for a fractional Kirchhoff type problem via Fountain Theorem (2015, result): “where M(t) = a+ bt for all t ≥ 0, here a, b > 0, see for instance [37,38,45] for recent results.”
A multiplicity result for asymptotically linear Kirchhoff equations (2017, background): “Zhang and Perera [33], and Mao and Zhang [17] obtained multiple and sign-changing solutions via the invariant sets of descent flow.”
Existence of a nodal solution with minimal energy for a Kirchhoff equation (2015, background): “In [24] the authors study the result found in [30] considering now the case asymptotically 3-linear.”
Existence and multiplicity of positive solutions for a class of Kirchhoff type problems with singularity (2015, background): “on a smooth bounded domain Ω ⊂ R and f : Ω × R → R a continuous function, has been extensively studied(see[1],[3],[10],[11],[15]-[20],[22],[23],[30]).”
Existence of a positive solution to Kirchhoff type problems without compactness conditions (2012, result): “has been studied by many authors, for example [2,4–6,8,12,13,19,20].”
Multiplicity of solutions for a class of Kirchhoff type problems (2010, background): “In [14] Mao and Zhang obtained a similar result as [ 18 ].”
Existence and multiplicity of solutions for Kirchhoff type problem with critical exponent (2013, methodology): “Sign-changing solutions are obtained by authors, such as Zhang and Perera [5], Mao ∗Supported by the National Natural Science Foundation of China ( No.”
Positive solutions to Kirchhoff type equations with nonlinearity having prescribed asymptotic behavior (2014, unknown): “1) with ν = 1 by using variational method, see for example, [1,3–5,10,11, 15–17,20,21,23].”