Existence and concentration behavior of positive solutions for a Kirchhoff equation in R3

By Xiaoming He, Wenming Zou. 2012

550 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/86b42c2117f2f21a1db275c9706e17f631be48c7

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In Applied Mathematics

In Computational Theory and Mathematics

In Control and Systems Engineering

Citations in the corpus

Multiplicity of high energy solutions for superlinear Kirchhoff equations (2012, background): “As far as we know, except a perturbation result in [26], there are no existence results when the potential and the coefficient of the nonlinearity are not symmetric and a not singularly perturbed problem is considered.”
On ground states for the Kirchhoff-type problem with a general critical nonlinearity (2015, background): “See, for example, [18] and [23].”
Existence and multiplicity of solutions for Kirchhoff type problem with critical exponent (2013, background): “And more recently the concentration behavior of positive solutions has been studied by He and Zou [12], Wang et al.”
Existence and concentration of positive ground states for a Kirchhoff equation involving critical Sobolev exponent (2014, background): “For problem (1.3) with b = 0, if f(x, u) = f(u) is a subcritical growth in (1.3) and V (x) satisfies the assumption (V) V ∈ C(R3,R+) and V∞ := lim inf|x|→∞ V (x) > V0 = infx∈R3 V (x) > 0, which is first introduced by Rabinowitz [41] in the study of a nonlinear Schrödinger equation with the nonlinea”
Study of a nonlinear Kirchhoff equation with non-homogeneous material (2014, background): “Multiplicity of solutions were showed in [11], [14], 2”
Concentrating Bound States for Kirchhoff Type Problems in ℝ3 Involving Critical Sobolev Exponents (2013, methodology): “Firstly, differently from [13] and [30], where only the ground states concentrating at the global minimum point of V (z) were obtained, we can construct a bound state which concentrates exactly at one point of any prescribed set consisting of local minimum points of V (z).”
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]).”
Normalized solutions to a class of Kirchhoff equations with Sobolev critical exponent (2021, background): “One can refer to [1, 6, 8, 12, 13, 20, 9] and the references therein for more mathematical and physical background of (1.”
A singularly perturbed Kirchhoff problem revisited (2016, background): “While in our proof, we derive all the positive solutions from a completely different way which is far more elementary than that of He and Zou [20], Ye [35] and Li and Ye [26].”
Existence of positive solutions for nonlinear Kirchhoff type problems in R3 with critical Sobolev exponent (2013, methodology): “3 can be viewed as a partial extension of a main result in [10].”
Existence and Concentration Result for the Kirchhoff Type Equations with General Nonlinearities (2014, background): “Therefore, our setting is different from those in [36,62] and we need refinements in order to find such a family of solutions.”