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 $$\begin{aligned} \left\{ \begin{array}{cl} M\left( \int _{\mathbb {R}^{2n}}\frac{|u(x)-u(y)|^p}{|x-y|^{n+sp}}\mathrm{d}x\mathrm{d}y\right) (-\triangle )_p^su+V(x)|u|^{p-2}u=f(x,u), &{}\quad \mathrm{in}~\Omega ,\\ u=0, &{}\quad \mathrm{in}~\mathbb… read more here.
Keywords: kirchhoff; solutions fractional; many solutions; infinitely many ... See more keywords
Positive Solutions and Infinitely Many Solutions for a Weakly Coupled System
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DOI: 10.1007/s10473-020-0523-9
Abstract: We study a Schrödinger system with the sum of linear and nonlinear couplings. Applying index theory, we obtain infinitely many solutions for the system with periodic potentials. Moreover, by using the concentration compactness method, we… read more here.
Keywords: system; solutions infinitely; positive solutions; solutions weakly ... See more keywords
Infinitely many meridional essential surfaces of bounded genus in hyperbolic knot exteriors
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DOI: 10.1007/s10711-021-00654-7
Abstract: We show the existence of an infinite collection of hyperbolic knots where each of which has in its exterior meridional essential planar surfaces of arbitrarily large number of boundary components, or, equivalently, that each of… read more here.
Keywords: essential surfaces; hyperbolic knot; meridional essential; infinitely many ... See more keywords
A Diophantine equation with the harmonic mean
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DOI: 10.1007/s10998-019-00302-4
Abstract: Let $$f\in \mathbb {Q}[x]$$ f ∈ Q [ x ] be a polynomial without multiple roots and $$\deg {f}\ge 2$$ deg f ≥ 2 . We give conditions for $$f=x^2+bx+c$$ f = x 2 +… read more here.
Keywords: diophantine equation; harmonic mean; infinitely many; equation harmonic ... See more keywords
Infinitely Many Solutions for Impulsive Nonlocal Elastic Beam Equations
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DOI: 10.1007/s12591-017-0397-z
Abstract: In this paper, we study the existence of solutions for impulsive beam equations of Kirchhoff-type. By using critical point theory, we obtain some new criteria for guaranteeing that impulsive fourth-order differential equations of Kirchhoff-type have… read more here.
Keywords: beam equations; many solutions; infinitely many; impulsive nonlocal ... See more keywords
Infinitely many solutions for a class of fractional Hamiltonian systems with combined nonlinearities
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DOI: 10.1007/s13324-017-0197-1
Abstract: This paper concerns the existence of infinitely many solutions for the following fractional Hamiltonian systems: $$\begin{aligned} \left\{ \begin{array}{lllll} -_{t}D^{\alpha }_{\infty }(_{-\infty }D^{\alpha }_{t}x(t))-L(t).x(t)+\nabla W(t,x(t))=0,\\ x\in H^{\alpha }({\mathbb R}, {\mathbb R}^{N}), \end{array} \right. \end{aligned}$$-tD∞α(-∞Dtαx(t))-L(t).x(t)+∇W(t,x(t))=0,x∈Hα(R,RN),where $$\alpha \in… read more here.
Keywords: alpha; infinitely many; hamiltonian systems; fractional hamiltonian ... See more keywords
Infinitely many sign-changing solutions to Kirchhoff-type equations
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DOI: 10.1007/s13324-018-0218-8
Abstract: In this paper we study the existence of multiple sign-changing solutions for the following nonlocal Kirchhoff-type boundary value problem: $$\begin{aligned} \left\{ \begin{array}{ll} -\left( a+b\int _{\Omega }|\nabla u|^2{ dx}\right) \triangle {u}=\lambda |u|^{p-1}u,&{}\quad \text{ in }\quad \Omega… read more here.
Keywords: kirchhoff type; infinitely many; sign changing; changing solutions ... See more keywords
A Loewner Equation for Infinitely Many Slits
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DOI: 10.1007/s40315-016-0179-6
Abstract: It is well-known that the growth of a slit in the upper half-plane can be encoded via the chordal Loewner equation, which is a differential equation for schlicht functions with a certain normalisation. We prove… read more here.
Keywords: equation infinitely; infinitely many; many slits; loewner equation ... See more keywords
Infinitely many solutions of fractional Schrödinger–Maxwell equations
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DOI: 10.1063/5.0028800
Abstract: In this article, we investigate the existence of infinitely many solutions to the 3D fractional Schrodinger–Maxwell equations (−Δ)su + V(x)u + ϕu = λf(x, u), (−Δ)sϕ = u2, where 0 < s < 1, λ… read more here.
Keywords: fractional schr; solutions fractional; many solutions; infinitely many ... See more keywords
Efficient moment-based approach to the simulation of infinitely many heterogeneous phase oscillators.
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DOI: 10.1063/5.0093001
Abstract: The dynamics of ensembles of phase oscillators are usually described considering their infinite-size limit. In practice, however, this limit is fully accessible only if the Ott-Antonsen theory can be applied, and the heterogeneity is distributed… read more here.
Keywords: phase oscillators; moment; based approach; moment based ... See more keywords
Infinitely Many Knots With NonIntegral Trace
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DOI: 10.1080/10586458.2021.1980461
Abstract: We prove that there are infinitely many non-homeomorphic hyperbolic knot complements $S^3\setminus K_i = \mathbb{H}^3/\Gamma_i$ for which $\Gamma_i$ contains elements whose trace is an algebraic non-integer. read more here.
Keywords: nonintegral trace; trace; many knots; infinitely many ... See more keywords