Nontrivial solutions of Kirchhoff-type problems via the Yang index
Kanishka Perera,Zhitao Zhang +1 more
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TLDR
In this paper, the Yang index and critical groups were used to obtain nontrivial solutions of a class of nonlocal quasilinear elliptic boundary value problems with respect to critical groups.About:
This article is published in Journal of Differential Equations.The article was published on 2006-02-01 and is currently open access. It has received 485 citations till now. The article focuses on the topics: Kirchhoff equations & Boundary value problem.read more
Citations
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Existence and concentration behavior of positive solutions for a Kirchhoff equation in R3
Xiaoming He,Wenming Zou +1 more
TL;DR: In this article, the existence, multiplicity and concentration behavior of positive solutions for the nonlinear Kirchhoff type problem is studied, where V is a positive continuous potential satisfying some conditions and f is a subcritical nonlinear term.
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Sign-changing and multiple solutions of Kirchhoff type problems without the P.S. condition
Anmin Mao,Zhitao Zhang +1 more
TL;DR: The existence of nontrivial solutions of 4-superlinear Kirchhoff type equations without the P.S. condition was studied in this article. But the existence of sign-changing solutions was not considered.
Journal ArticleDOI
Existence of a positive solution to Kirchhoff type problems without compactness conditions
TL;DR: The existence of a positive solution to a Kirchhoff type problem on R N is proved by using variational methods, and the new result does not require usual compactness conditions as discussed by the authors.
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Multiplicity and concentration of positive solutions for a Kirchhoff type problem with critical growth
TL;DR: In this article, the multiplicity and concentration of positive solutions for the semilinear Kirchhoff type equation were studied and the relation between the number of positive ground state solutions and the topology of the set of the global minima of the potentials by minimax theorems and the Ljusternik-Schnirelmann theory was investigated.
Journal ArticleDOI
Infinitely many positive solutions for Kirchhoff-type problems
TL;DR: In this paper, Zhang et al. showed that the existence of infinitely many positive solutions to a class of Kirchhoff-type problems can be found in L ∞ ( Ω ), where Ω is a smooth bounded domain of R N, a, b > 0, λ > 0.
References
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Book
Partial Differential Equations
TL;DR: In this paper, the authors present a theory for linear PDEs: Sobolev spaces Second-order elliptic equations Linear evolution equations, Hamilton-Jacobi equations and systems of conservation laws.
Book ChapterDOI
On Some Questions in Boundary Value Problems of Mathematical Physics
TL;DR: In this article, the boundary value problems of non-homogeneous fluids have been studied and the existence of strong solutions in the two-dimensional case has been shown to be true.
Journal ArticleDOI
Positive solutions for a quasilinear elliptic equation of Kirchhoff type
TL;DR: In this article, the existence of positive solutions to the class of nonlocal boundary value problems of the type -M(@!"@W|@?u|^2dx)@Du=f(x,u),[email protected],u=0,[email protected][email protected] was studied.
Journal ArticleDOI
On the Well-Posedness of the Kirchhoff String
Alberto Arosio,Stefano Panizzi +1 more
TL;DR: In this article, the Cauchy problem for the quasilinear hyperbolic integro-differential equation is considered for the case of a quasileinear QDE.
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