Existence of positive solutions for a critical fractional Kirchhoff equation with potential vanishing at infinity
Sign Up to like & getrecommendations! Published in 2021 at "Mathematische Nachrichten"
DOI: 10.1002/mana.201900273
Abstract: In this paper, we consider the following fractional Kirchhoff equation with critical nonlinearity a+b∫R3(−Δ)s2u2dx(−Δ)su+V(x)u=Q(x)f(u)+|u|2s∗−2u,x∈R3,where a,b>0 , (−Δ)s is the fractional Laplace operator with s∈(34,1) , V vanishes at infinity and 2s∗=63−2s . Under appropriate assumptions… read more here.
Keywords: kirchhoff equation; existence positive; fractional kirchhoff; infinity ... See more keywords
Blow-up and Lifespan of Solutions for a Nonlinear Viscoelastic Kirchhoff Equation
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DOI: 10.1007/s00025-020-01223-2
Abstract: The blow-up of solutions of a class of nonlinear viscoelastic Kirchhoff equation with suitable initial data and Dirichlet boundary conditions is discussed. By constructing a suitable auxiliary function to overcome the difficulty of gradient estimation… read more here.
Keywords: kirchhoff equation; nonlinear viscoelastic; blow lifespan; viscoelastic kirchhoff ... See more keywords
Multiplicity of concentrating solutions for a class of fractional Kirchhoff equation
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DOI: 10.1007/s00229-018-1017-0
Abstract: We study the multiplicity of concentrating solutions to the nonlinear fractional Kirchhoff equation $$\begin{aligned} \left( \varepsilon ^{2s}a+\varepsilon ^{4s-3}b\int _{\mathbb R^3}|(-\Delta )^{\frac{s}{2}}u|^2dx\right) (-\Delta )^s u+V(x)u=f(u)~~\text{ in }~~\mathbb R^3, \end{aligned}$$ε2sa+ε4s-3b∫R3|(-Δ)s2u|2dx(-Δ)su+V(x)u=f(u)inR3,where $$\varepsilon >0$$ε>0 is a positive parameter, $$(-\Delta… read more here.
Keywords: fractional kirchhoff; concentrating solutions; multiplicity concentrating; kirchhoff equation ... See more keywords
Almost global well-posedness of Kirchhoff equation with Gevrey data
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DOI: 10.1016/j.crma.2017.04.001
Abstract: Abstract The aim of this note is to present the almost global well-posedness result for the Cauchy problem for the Kirchhoff equation with large data in Gevrey spaces. We also briefly discuss the corresponding results… read more here.
Keywords: kirchhoff equation; global well; well posedness; almost global ... See more keywords
Global existence of solutions to a viscoelastic non-degenerate Kirchhoff equation
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DOI: 10.1080/00036811.2018.1544621
Abstract: ABSTRACT In this paper, a nonlinear viscoelastic kirchhoff equation in a bounded domain with a time varying delay in the weakly nonlinear internal feedback is considered, where the global existence of solutions in suitable Sobolev… read more here.
Keywords: global existence; kirchhoff equation; existence solutions;
Quasi-periodic solutions for the forced Kirchhoff equation on $T^d$
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DOI: 10.1088/1361-6544/aad6fe
Abstract: In this paper we prove the existence of small-amplitude quasi-periodic solutions with Sobolev regularity, for the d-dimensional forced Kirchhoff equation with periodic boundary conditions. This is the first result of this type for a quasi-linear… read more here.
Keywords: solutions forced; kirchhoff equation; periodic solutions; forced kirchhoff ... See more keywords
The existence of positive solution for singular Kirchhoff equation with two parameters
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DOI: 10.1186/s13661-019-1154-8
Abstract: AbstractIn this paper, we consider the singular Kirchhoff equation with two parameters {−a(∫Ω|∇u(x)|2dx)△u(x)+K(x)g(u)=λf(x,u)+μh(x)in Ω,u>0in Ω,u=0on ∂Ω.$$\textstyle\begin{cases} -a ( \int_{\varOmega}|\nabla u(x)|^{2}\,dx )\triangle u(x)+K(x)g(u)=\lambda f(x,u)+\mu h(x) \quad \mbox{in } \varOmega, \\ u>0 \quad \mbox{in } \varOmega, \\ u=0 \quad \mbox{on… read more here.
Keywords: two parameters; kirchhoff equation; singular kirchhoff; equation two ... See more keywords
Existence of ground state for fractional Kirchhoff equation with $L^{2}$ critical exponents
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DOI: 10.1186/s13661-020-01424-2
Abstract: In this paper, we consider a class of fractional Kirchhoff equations with $L^{2}$ critical exponents. By using the scaling technique and concentration-compactness principle we obtain the existence and nonexistence of ground state for fractional Kirchhoff… read more here.
Keywords: state fractional; kirchhoff equation; kirchhoff; fractional kirchhoff ... See more keywords