共查询到20条相似文献,搜索用时 15 毫秒
1.
We investigate the non-homogeneous modular Dirichlet problem Δ p (·)u(x) = f (x) (where Δ p (·)u(x) = div(|?u|p(x-2)?u(x)) from the functional analytic point of view and we prove the stability of the solutions \({\left( {{u_{{p_i}}}} \right)_i}\) of the equation \({\Delta _{{p_i}\left( \cdot \right)}}{u_{{p_i}\left( \cdot \right)}} = f\) as p i (·) → q(·) via Gamma-convergence of sequence of appropriate functionals. 相似文献
2.
This paper studies heat equation with variable exponent u t = Δu + up(x) + u q in ? N × (0, T), where p(x) is a nonnegative continuous, bounded function, 0 < p? = inf p(x) ≤ p(x) ≤ sup p(x) = p+. It is easy to understand for the problem that all nontrivial nonnegative solutions must be global if and only if max {p+, q} ≤ 1. Based on the interaction between the two sources with fixed and variable exponents in the model, some Fujita type conditions are determined that that all nontrivial nonnegative solutions blow up in finite time if 0 < q ≤ 1 with p+ > 1, or 1 < q < 1 + \(\frac{2}{N}\). In addition, if q > 1 + \(\frac{2}{N}\), then (i) all solutions blow up in finite time with 0 < p? ≤ p+ ≤ 1 + \(\frac{2}{N}\); (ii) there are both global and nonglobal solutions for p? > 1 + \(\frac{2}{N}\); and (iii) there are functions p(x) such that all solutions blow up in finite time, and also functions p(x) such that the problem possesses global solutions when p? < 1 + \(\frac{2}{N}\) < p+. 相似文献
3.
For any operator defined by the differential operation Lu = ?u″ + q(x)u on the interval G = (0, 1) with complex-valued potential q(x) locally integrable on G and satisfying the inequalities \(\int_{{x_1}}^{{x_2}} {\zeta |(q(\zeta ))|d\zeta \leqslant ln({x_1}/{x_2})} \) and \(\int_{{x_1}}^{{x_2}} {\zeta |(q(1 - \zeta ))|d\zeta \leqslant \gamma ln({x_1}/{x_2})} \) with some constant γ for all sufficiently small 0 < x1 < x2, we estimate the norms of root functions in the Lebesgue spaces L p (G), 1 ≤ p < ∞. We show that for sufficiently small γ these norms satisfy the same estimates asymptotic in the spectral parameter as in the unperturbed case. 相似文献
4.
Let G be a nonabelian group, and associate the noncommuting graph ?(G) with G as follows: the vertex set of ?(G) is G\Z(G) with two vertices x and y joined by an edge whenever the commutator of x and y is not the identity. Let S 4(q) be the projective symplectic simple group, where q is a prime power. We prove that if G is a group with ?(G) ? ?(S 4(q)) then G ? S 4(q). 相似文献
5.
O. A. Alekseeva A. S. Kondrat’ev 《Proceedings of the Steklov Institute of Mathematics》2009,266(1):10-23
It is proved that, if G is a finite group that has the same set of element orders as the simple group D p (q), where p is prime, p ≥ 5 and q ∈ {2, 3, 5}, then the commutator group of G/F(G) is isomorphic to D p (q), the subgroup F(G) is equal to 1 for q = 5 and to O q (G) for q ∈ {2, 3}, F(G) ≤ G′, and |G/G′| ≤ 2. 相似文献
6.
We prove the monotonicity of nonnegative bounded solutions of the Dirichlet problem for the quasilinear elliptic equation ?Δpu = f(u), p ≥ 3, in a half-space. This assertion implies new results on the nonexistence of solutions for the case in which f(u) = uq with appropriate values of q. 相似文献
7.
This paper is devoted to a study of L~q-tracing of the fractional temperature field u(t, x)—the weak solution of the fractional heat equation(?_t +(-?_x)~α)u(t, x) = g(t, x) in L~p(R_+~(1+n)) subject to the initial temperature u(0, x) = f(x) in L~p(R~n). 相似文献
8.
The completeness, minimality, and basis property in L 2[0, π] and L p[0, π], p ≠ 2, are considered for systems of dilated functions u n (x) = S(nx), n ∈ N, where S is the trigonometric polynomial S(x) = Σ k=0 m a k sin(kx), a 0 a m ≠ 0. A series of results are presented and several unanswered questions are mentioned. 相似文献
9.
Assume that G is a primitive permutation group on a finite set X, x ∈ X, y ∈ X \ {x}, and G x,y \(\underline \triangleleft \) G x . P. Cameron raised the question about the validity of the equality G x,y = 1 in this case. The author proved earlier that, if soc(G) is not a direct power of an exceptional group of Lie type, then G x,y = 1. In the present paper, we prove that, if soc(G) is a direct power of an exceptional group of Lie type distinct from E 6(q), 2 E 6(q), E 7(q), and E 8(q), then G x,y = 1. 相似文献
10.
The aim of this paper is to investigate the relations between Seifert manifolds and (1, 1)-knots. In particular, we prove that each orientable Seifert manifold with invariants has the fundamental group cyclically presented by G n ((x 1 q ...x n q l x n ?p ) and, moreover, it is the n-fold strongly-cyclic covering of the lens space L(|nlq ? p|, q) which is branched over the (1, 1)-knot K(q, q(nl ? 2), p ? 2q, p ? q) if p ≥ 2q and over the (1, 1)-knot K(p? q, 2q ? p, q(nl ? 2), p ? q) if p< 2q.
相似文献
$\{ Oo,0| - 1;\underbrace {(p,q),...,(p,q)}_{n times},(l,l - 1)\} $
11.
A. Vera-López J. M. Arregi Leyre Ormaetxea F. J. Vera-López Olga Basova 《Israel Journal of Mathematics》2016,214(2):675-697
We denote by Gn the group of the upper unitriangular matrices over Fq, the finite field with q = pt elements, and r(Gn) the number of conjugacy classes of Gn. In this paper, we obtain the value of r(Gn) modulo (q2 -1)(q -1). We prove the following equalities 相似文献
12.
Let u =(uh, u3) be a smooth solution of the 3-D Navier-Stokes equations in R3× [0, T). It was proved that if u3 ∈ L∞(0, T;˙B-1+3/p p,q(R3)) for 3 p, q ∞ and uh∈ L∞(0, T; BMO-1(R3)) with uh(T) ∈ VMO-1(R3), then u can be extended beyond T. This result generalizes the recent result proved by Gallagher et al.(2016), which requires u ∈ L∞(0, T;˙B-1+3/pp,q(R3)). Our proof is based on a new interior regularity criterion in terms of one velocity component, which is independent of interest. 相似文献
13.
The properties of the root functions are studied for an arbitrary operator generated in L 2(?1, 1) by the operation with involution of the form Lu = ?u″(x)+αu″(?x)+q(x)u(x)+ qν(x)u(ν(x)), where α ∈ (?1, 1), ν(x) is an absolutely continuous involution of the segment [?1, 1] and the coefficients q(x) and qν(x) are summable functions on (?1, 1). Necessary and sufficient conditions are obtained for the unconditional basis property in L 2(?1, 1) for the system of the root functions of the operator. 相似文献
14.
We consider the quasilinear Schrödinger equations of the form ?ε2Δu + V(x)u ? ε2Δ(u2)u = g(u), x∈ RN, where ε > 0 is a small parameter, the nonlinearity g(u) ∈ C1(R) is an odd function with subcritical growth and V(x) is a positive Hölder continuous function which is bounded from below, away from zero, and infΛV(x) < inf?ΛV(x) for some open bounded subset Λ of RN. We prove that there is an ε0 > 0 such that for all ε ∈ (0, ε0], the above mentioned problem possesses a sign-changing solution uε which exhibits concentration profile around the local minimum point of V(x) as ε → 0+. 相似文献
15.
I. V. Sadovnichaya 《Differential Equations》2008,44(5):675-684
We study the Sturm-Liouville operator L = ?d 2/dx 2 + q(x) in the space L 2[0, π] with the Dirichlet boundary conditions. We assume that the potential has the form q(x) = u′(x), u ∈ W 2 θ [0, π], 0 < θ < 1/2. We consider the problem on the uniform (on the entire interval [0, π]) equiconvergence of the expansion of a function f(x) in a series in the system of root functions of the operator L with its Fourier expansion in the system of sines. We show that if the antiderivative u(x) of the potential belongs to any of the spaces W 2 θ [0, π], 0 < θ < 1/2, then the equiconvergence rate can be estimated uniformly over the ball u(x) ∈ B R = {v(x) ∈ W 2 θ [0, π] | ∥v∥W 2 θ ≤ R} for any function f(x) ∈ L 2[0, π]. 相似文献
16.
A. I. Aristov 《Differential Equations》2018,54(9):1137-1146
The equation ?2u/?t?x + up?u/?x = uq describing a nonstationary process in semiconductors, with parameters p and q that are a nonnegative integer and a positive integer, respectively, and satisfy p + q ≥ 2, is considered in the half-plane (x, t) ∈ ? × (0,∞). All in all, fourteen families of its exact solutions are constructed for various parameter values, and qualitative properties of these solutions are noted. One of these families is defined for all parameter values indicated above. 相似文献
17.
Let G be a finite group. The main result of this paper is as follows: If G is a finite group, such that Γ(G) = Γ(2G2(q)), where q = 32n+1 for some n ≥ 1, then G has a (unique) nonabelian composition factor isomorphic to 2 G 2(q). We infer that if G is a finite group satisfying |G| = |2 G 2(q)| and Γ(G) = Γ (2 G 2(q)) then G ? = 2 G 2(q). This enables us to give new proofs for some theorems; e.g., a conjecture of W. Shi and J. Bi. Some applications of this result are also considered to the problem of recognition by element orders of finite groups. 相似文献
18.
Based on the eigensystem {λj,φj} of -Δ, the multiple solutions for nonlinear problem Δu + f(u) = 0 in Ω,u = 0 on ?Ω are approximated. A new search-extension method (SEM), which consists of three steps in three level subspaces, is proposed. Numerical simulations for several typical nonlinear cases, i.e. f(u) = u 3, u 2, (u - p), u 2(u 2 - p), are completed and some conjectures are presented. 相似文献
19.
O. Yu. Khachay 《Differential Equations》2008,44(2):282-285
We consider the Cauchy problem for the nonlinear differential equation where ? > 0 is a small parameter, f(x, u) ∈ C ∞ ([0, d] × ?), R 0 > 0, and the following conditions are satisfied: f(x, u) = x ? u p + O(x 2 + |xu| + |u|p+1) as x, u → 0, where p ∈ ? \ {1} f(x, 0) > 0 for x > 0; f u 2(x, u) < 0 for (x, u) ∈ [0, d] × (0, + ∞); Σ 0 +∞ f u 2(x, u) du = ?∞. We construct three asymptotic expansions (external, internal, and intermediate) and prove that the matched asymptotic expansion approximates the solution uniformly on the entire interval [0, d].
相似文献
$$\varepsilon \frac{{du}}{{dx}} = f(x,u),u(0,\varepsilon ) = R_0 ,$$
20.
N. P. Trotsenko 《Computational Mathematics and Mathematical Physics》2017,57(6):967-977
For the equation χ″(x) = u(x)χ(x) with infinitely smooth u(x), the general solution χ(x) is found in the form of a power series. The coefficients of the series are expressed via all derivatives u (m)(y) of the function u(x) at a fixed point y. Examples of solutions for particular functions u(x) are considered. 相似文献