Multiplicity Results for Kirchhoff Equations with Hardy-Littlewood-Sobolev Critical Nonlinearity
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DOI: 10.1007/s10883-019-09456-3
Abstract: In this paper, we deal with the multiplicity results for Kirchhoff equations with Hardy-Littlewood-Sobolev critical nonlinearity in ℝ N $\mathbb {R}^{N}$ . By using the second concentration-compactness principle and concentration-compactness principle at infinity to prove… read more here.
Keywords: equations hardy; hardy littlewood; littlewood sobolev; results kirchhoff ... See more keywords
On a class of Kirchhoff equations involving an anisotropic operator and potential
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DOI: 10.1007/s40065-020-00304-y
Abstract: In this work, we are concerned with a class of fractional equations of Kirchhoff type with potential. Using variational methods and a variant of quantitative deformation lemma, we prove the existence of a least energy… read more here.
Keywords: anisotropic operator; class kirchhoff; class; kirchhoff equations ... See more keywords
Positive solutions to Schrödinger-Kirchhoff equations with inverse potential
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DOI: 10.1080/17476933.2020.1843642
Abstract: This paper is concerned with the existence of positive solutions to Schrödinger-Kirchhoff-type equations where a and b are two positive constants, and is a potential function. Under certain assumptions on V, we prove that has… read more here.
Keywords: positive solutions; dinger kirchhoff; schr dinger; solutions schr ... See more keywords
Bound states for fractional Kirchhoff equations with critical growth
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DOI: 10.1080/17476933.2024.2418854
Abstract: This paper deals with the following fractional Kirchhoff problems: $$\begin{align*} &\left(\varepsilon^{2s}a+\varepsilon^{4s-N}b\int_{\Bbb R^N}|(-\Delta)^{\frac{s}{2}}u|^2\,{\rm d}x\right)(-\Delta )^su+V(x)u\notag \\ &\quad =|u|^{2^{*}_{s}-2}u,\quad {\rm in}\ \Bbb R^N, \end{align*} $$(ε2sa+ε4s−Nb∫RN|(−Δ)s2u|2dx)(−Δ)su+V(x)u=|u|2s∗−2u,inRN, where a, b>0, $ s\in (0,1) $ s∈(0,1), 2s read more here.
Keywords: equations critical; states fractional; fractional kirchhoff; bound states ... See more keywords
Solutions with prescribed mass to Kirchhoff equations: generic double-behaviour nonlinearities
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DOI: 10.1088/1361-6544/ae0b26
Abstract: In this paper, we study the Kirchhoff equation {−(a+b∫ℝ3|∇u|2dx)Δu+λu=f(u), x∈ℝ3,∫ℝ3|u|2dx=c2, x∈ℝ3,(λ,u)∈ℝ×H1(ℝ3), where a,b,c>0, λ∈R is unknown as a Lagrange multiplier. We provide generic assumptions about the nonlinearity f(u), which correspond to the L2-subcritical, L2-critical, L2-supercritical, and Sobolev… read more here.
Keywords: equations generic; generic double; mass kirchhoff; solutions prescribed ... See more keywords
Invariant relations for kirchhoff equations and the Kowalewski method
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DOI: 10.1134/s1028335817010013
Abstract: The Kowalewski exponents in the problem on the motion of a solid under the Chaplygin condition are calculated (when there is a velocity-linear invariant relation). The method of calculation uses the generalizing Ioshida theorems on… read more here.
Keywords: relations kirchhoff; equations kowalewski; kirchhoff equations; method ... See more keywords