共查询到20条相似文献,搜索用时 105 毫秒
1.
Vincenzo Ambrosio Hichem Hajaiej 《Journal of Dynamics and Differential Equations》2018,30(3):1119-1143
This paper is concerned with the following fractional Schrödinger equation where \(s\in (0,1),N> 2s, (-\Delta )^{s}\) is the fractional Laplacian, k is a bounded positive function, \(h\in L^{2}(\mathbb {R}^{N}), h\not \equiv 0\) is nonnegative and f is either asymptotically linear or superlinear at infinity. By using the s-harmonic extension technique and suitable variational methods, we prove the existence of at least two positive solutions for the problem under consideration, provided that \(|h|_{2}\) is sufficiently small.
相似文献
$$\begin{aligned} \left\{ \begin{array}{ll} (-\Delta )^{s} u+u= k(x)f(u)+h(x) \text{ in } \mathbb {R}^{N}\\ u\in H^{s}(\mathbb {R}^{N}), \, u>0 \text{ in } \mathbb {R}^{N}, \end{array} \right. \end{aligned}$$
2.
We prove that, if ${u : \Omega \subset \mathbb{R}^n \to \mathbb{R}^N}We prove that, if
u : W ì \mathbbRn ? \mathbbRN{u : \Omega \subset \mathbb{R}^n \to \mathbb{R}^N} is a solution to the Dirichlet variational problem
minwòW F(x, w, Dw) dx subject to w o u0 on ?W,\mathop {\rm min}\limits_{w}\int_{\Omega} F(x, w, Dw)\,{\rm d}x \quad {\rm subject \, to} \quad w \equiv u_0\; {\rm on}\;\partial \Omega, 相似文献
3.
Peter Hornung 《Archive for Rational Mechanics and Analysis》2011,199(3):1015-1067
Let \({S\subset\mathbb{R}^2}\) be a bounded Lipschitz domain and denote by \({W^{2,2}_{\text{iso}}(S; \mathbb{R}^3)}\) the set of mappings \({u\in W^{2,2}(S;\mathbb{R}^3)}\) which satisfy \({(\nabla u)^T(\nabla u) = Id}\) almost everywhere. Under an additional regularity condition on the boundary \({\partial S}\) (which is satisfied if \({\partial S}\) is piecewise continuously differentiable), we prove that the strong W 2,2 closure of \({W^{2,2}_{\text{iso}}(S; \mathbb{R}^3)\cap C^{\infty}(\overline{S};\mathbb{R}^3)}\) agrees with \({W^{2,2}_{\text{iso}}(S; \mathbb{R}^3)}\). 相似文献
4.
Stationary Solutions and Connecting Orbits for <Emphasis Type="Italic">p</Emphasis>-Laplace Equation
Aleksander Ćwiszewski Mateusz Maciejewski 《Journal of Dynamics and Differential Equations》2018,30(1):309-329
We deal with one dimensional p-Laplace equation of the form 相似文献
$$\begin{aligned} u_t = (|u_x|^{p-2} u_x )_x + f(x,u), \ x\in (0,l), \ t>0, \end{aligned}$$ 5.
We consider the following nonlinear Schrödinger system in ${\mathbb{R}^3}$ $$\left\{\begin{array}{ll}-\Delta u + P(|x|)u = \mu u^{2}u + \beta v^2u,\quad x \in \mathbb{R}^3,\\-\Delta v + Q(|x|)v = \nu v^{2}v + \beta u^2v,\quad x \in \mathbb{R}^3,\end{array}\right.$$ where P(r) and Q(r) are positive radial potentials, ${\mu > 0, \nu > 0}$ and ${\beta \in \mathbb{R}}$ is a coupling constant. This type of system arises, in particular, in models in Bose–Einstein condensates theory. We examine the effect of nonlinear coupling on the solution structure. In the repulsive case, we construct an unbounded sequence of non-radial positive vector solutions of segregated type, and in the attractive case we construct an unbounded sequence of non-radial positive vector solutions of synchronized type. Depending upon the system being repulsive or attractive, our results exhibit distinct characteristic features of vector solutions. 相似文献
6.
F. Micena 《Journal of Dynamics and Differential Equations》2017,29(3):1159-1172
In this paper we focused our study on derived from Anosov diffeomorphisms (DA diffeomorphisms ) of the torus \(\mathbb {T}^3,\) it is, an absolute partially hyperbolic diffeomorphism on \(\mathbb {T}^3\) homotopic to a linear Anosov automorphism of the \(\mathbb {T}^3.\) We can prove that if \(f: \mathbb {T}^3 \rightarrow \mathbb {T}^3 \) is a volume preserving DA diffeomorphism homotopic to a linear Anosov A, such that the center Lyapunov exponent satisfies \(\lambda ^c_f(x) > \lambda ^c_A > 0,\) with x belongs to a positive volume set, then the center foliation of f is non absolutely continuous. We construct a new open class U of non Anosov and volume preserving DA diffeomorphisms, satisfying the property \(\lambda ^c_f(x) > \lambda ^c_A > 0\) for \(m-\)almost everywhere \(x \in \mathbb {T}^3.\) Particularly for every \(f \in U,\) the center foliation of f is non absolutely continuous. 相似文献
7.
Fix a strictly increasing right continuous with left limits function ${W: \mathbb{R} \to \mathbb{R}}
8.
Existence of Weak Solutions to the Equations of Non-Stationary Motion of Non-Newtonian Fluids with Shear Rate Dependent Viscosity 总被引:1,自引:0,他引:1
Jörg Wolf 《Journal of Mathematical Fluid Mechanics》2007,9(1):104-138
In the present paper we prove the existence of weak solutions
to the equations of non-stationary motion of an incompressible fluid with shear rate dependent viscosity in a cylinder Q = Ω × (0,T), where
denotes an open set. For the power-low model with
we are able to construct a weak solution
with ∇ · u = 0. 相似文献
9.
We consider the Cauchy problem for incompressible Navier–Stokes equations
with initial data in
, and study in some detail the smoothing effect of the equation. We prove that for T < ∞ and for any positive integers n and m we have
, as long as
stays finite. 相似文献
10.
S. H. Saker 《Nonlinear Oscillations》2011,13(3):407-428
Our aim is to establish some sufficient conditions for the oscillation of the second-order quasilinear neutral functional
dynamic equation
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