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 $$\begin{aligned} \left\{ \begin{array}{cl} M\left( \int _{\mathbb {R}^{2n}}\frac{|u(x)-u(y)|^p}{|x-y|^{n+sp}}\mathrm{d}x\mathrm{d}y\right) (-\triangle )_p^su+V(x)|u|^{p-2}u=f(x,u), &{}\quad \mathrm{in}~\Omega ,\\ u=0, &{}\quad \mathrm{in}~\mathbb… read more here.
Keywords: kirchhoff; solutions fractional; many solutions; infinitely many ... See more keywords
Positive Solutions and Infinitely Many Solutions for a Weakly Coupled System
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DOI: 10.1007/s10473-020-0523-9
Abstract: We study a Schrödinger system with the sum of linear and nonlinear couplings. Applying index theory, we obtain infinitely many solutions for the system with periodic potentials. Moreover, by using the concentration compactness method, we… read more here.
Keywords: system; solutions infinitely; positive solutions; solutions weakly ... See more keywords
Many solutions to the S-unit equation $$a + 1 = c$$
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DOI: 10.1007/s10474-019-00948-z
Abstract: We show that there are arbitrarily large sets $S$ of $s$ primes for which the number of solutions to $a+1=c$ where all prime factors of $ac$ lie in $S$ has $\gg \exp( s^{1/4}/\log s)$ solutions. read more here.
Keywords: solutions unit; unit equation; many solutions;
Infinitely Many Solutions for Impulsive Nonlocal Elastic Beam Equations
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DOI: 10.1007/s12591-017-0397-z
Abstract: In this paper, we study the existence of solutions for impulsive beam equations of Kirchhoff-type. By using critical point theory, we obtain some new criteria for guaranteeing that impulsive fourth-order differential equations of Kirchhoff-type have… read more here.
Keywords: beam equations; many solutions; infinitely many; impulsive nonlocal ... See more keywords
Infinitely many solutions for a class of fractional Hamiltonian systems with combined nonlinearities
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DOI: 10.1007/s13324-017-0197-1
Abstract: This paper concerns the existence of infinitely many solutions for the following fractional Hamiltonian systems: $$\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 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
Infinitely many solutions for a class of stationary Schrödinger equations with non-standard growth
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DOI: 10.1080/17476933.2017.1322074
Abstract: In this paper, we study the existence of infinitely many solutions for a class of stationary Schrödinger type equations in involving the p(x)-Laplacian. The non-linearity is superlinear but does not satisfy the Ambrosetti-Rabinowitz type condition.… read more here.
Keywords: class stationary; solutions class; many solutions; stationary schr ... See more keywords
Infinitely Many Solutions of Schrödinger-Poisson Equations with Critical and Sublinear Terms
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DOI: 10.1155/2019/8453176
Abstract: Faculty of Applied Mathematics, Shanxi University of Finance and Economics, Taiyuan, Shanxi 030006, China College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China Department of Mathematics, North University of China, Taiyuan, Shanxi 030051, China… read more here.
Keywords: mathematics; dinger poisson; many solutions; infinitely many ... See more keywords
Infinitely many solutions for fractional Schrödinger equation with potential vanishing at infinity
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DOI: 10.1186/s13661-019-1175-3
Abstract: AbstractThe paper investigates the following fractional Schrödinger equation: (−Δ)su+V(x)u=K(x)f(u),x∈RN, $$\begin{aligned} (-\Delta )^{s}u+V(x)u=K(x)f(u), \quad x\in \mathbb{R}^{N}, \end{aligned}$$ where 0 read more here.
Keywords: schr dinger; infinitely many; dinger equation; many solutions ... See more keywords
Remarks on infinitely many solutions for a class of Schrödinger equations with sign-changing potential
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DOI: 10.1186/s13661-020-01356-x
Abstract: In this paper, we study the existence of infinitely many nontrivial solutions for the following semilinear Schrödinger equation: { − Δ u + V ( x ) u = f ( x , u )… read more here.
Keywords: remarks infinitely; many solutions; infinitely many; sign changing ... See more keywords
Existence of infinitely many solutions for a p-Kirchhoff problem in RN
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DOI: 10.1186/s13661-020-01403-7
Abstract: We consider the existence of multiple solutions of the following singular nonlocal elliptic problem: $$\begin{aligned} \textstyle\begin{cases} -M(\int _{\mathbb{R} ^{N}}{ \vert x \vert ^{-ap} \vert \nabla u \vert ^{p}})\operatorname{div}( \vert x \vert ^{-ap} \vert \nabla u… read more here.
Keywords: many solutions; infinitely many; vert; vert nabla ... See more keywords