Existence of positive solutions for a critical fractional Kirchhoff equation with potential vanishing at infinity
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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
Infinitely Many Solutions for Fractional p-Kirchhoff Equations
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DOI: 10.1007/s00009-018-1124-x
Abstract: In this paper we consider the existence of infinitely many weak solutions for fractional Schrödinger–Kirchhoff problems. Precisely speaking, we investigate $$\begin{aligned} \left\{ \begin{array}{cl} M\left( \int _{\mathbb {R}^{2n}}\frac{|u(x)-u(y)|^p}{|x-y|^{n+sp}}\mathrm{d}x\mathrm{d}y\right) (-\triangle )_p^su+V(x)|u|^{p-2}u=f(x,u), &{}\quad \mathrm{in}~\Omega ,\\ u=0, &{}\quad \mathrm{in}~\mathbb… read more here.
Keywords: kirchhoff; solutions fractional; many solutions; infinitely many ... See more keywords
Multiplicity of concentrating solutions for a class of fractional Kirchhoff equation
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DOI: 10.1007/s00229-018-1017-0
Abstract: We study the multiplicity of concentrating solutions to the nonlinear fractional Kirchhoff equation $$\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
Existence of solutions for a critical fractional Kirchhoff type problem in ℝN
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DOI: 10.1007/s11425-015-0792-2
Abstract: This paper concerns with the existence of solutions for the following fractional Kirchhoff problem with critical nonlinearity: $${\left( {\int {\int {_{{\mathbb{R}^{2N}}}\frac{{{{\left| {u\left( x \right) - u\left( y \right)} \right|}^2}}}{{{{\left| {x - y} \right|}^{N + 2s}}}}dxdy}… read more here.
Keywords: left right; solutions critical; fractional kirchhoff; problem ... See more keywords
Existence and non-existence results for fractional Kirchhoff Laplacian problems
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DOI: 10.1007/s13324-020-00435-7
Abstract: In this paper, we study the following fractional Kirchhoff-type problem: $$\begin{aligned} \left[ a+b\Big (\iint _{{\mathbb {R}}^{2N}} \frac{|u(x)-u(y)|^2}{|x-y|^{N+2s}}dx dy \Big )^{\theta -1}\right] (-\Delta )^s u= & {} |u|^{2^*_s- 2} u\\&\quad + \lambda f(x) |u|^{q-2}u, ~ in… read more here.
Keywords: fractional kirchhoff; existence non; existence; existence results ... See more keywords
Nehari-type ground state solutions for asymptotically periodic fractional Kirchhoff-type problems in RN$\mathbb{R}^{N}$
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DOI: 10.1186/s13661-017-0922-6
Abstract: AbstractIn this paper, we studied the following fractional Kirchhoff-type equation: (a+b∫RN|(−△)α2u|2dx)(−△)αu+V(x)u=f(x,u),x∈RN,$$\biggl(a+b \int_{\mathbb{R}^{N}} \bigl\vert (-\triangle)^{\frac{\alpha }{2}}u \bigr\vert ^{2}\,\mathrm{d}x \biggr) (-\triangle)^{\alpha }u+V(x)u=f(x,u), \quad x\in{\mathbb{R}}^{N}, $$ where a, b are positive constants, α∈(0,1)$\alpha\in(0,1)$, N∈(2α,4α)$N\in (2\alpha,4\alpha)$, (−△)α$(-\triangle)^{\alpha}$ is the… read more here.
Keywords: fractional kirchhoff; asymptotically periodic; state solutions; type ... 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
Infinitely many solutions for fractional Kirchhoff–Sobolev–Hardy critical problems
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DOI: 10.14232/ejqtde.2019.1.25
Abstract: We investigate a class of critical stationary Kirchhoff fractional p-Laplacian problems in presence of a Hardy potential. By using a suitable version of the symmetric mountain-pass lemma due to Kajikiya, we obtain the existence of… read more here.
Keywords: infinitely many; solutions fractional; kirchhoff sobolev; fractional kirchhoff ... See more keywords
Fractional Kirchhoff-type problems with exponential growth without the Ambrosetti–Rabinowitz condition
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DOI: 10.1515/ijnsns-2019-0171
Abstract: Abstract The main aim of this paper is to investigate the existence of nontrivial solutions for a class of fractional Kirchhoff-type problems with right-hand side nonlinearity which is subcritical or critical exponential growth (subcritical polynomial… read more here.
Keywords: kirchhoff type; growth; exponential growth; ambrosetti rabinowitz ... See more keywords
Multiplicity and concentration of positive solutions to the fractional Kirchhoff type problems involving sign-changing weight functions
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DOI: 10.3934/cpaa.2021096
Abstract: The aim of this paper is to study the multiplicity and concentration of positive solutions to the fractional Kirchhoff type problems involving sign-changing weight functions and concave-convex nonlinearities with subcritical or critical growth. Applying Nehari… read more here.
Keywords: concentration positive; kirchhoff type; multiplicity concentration; positive solutions ... See more keywords