共查询到20条相似文献,搜索用时 250 毫秒
1.
In this paper we consider the weakly coupled elliptic system with critical growth
where a, b, c, d are C
1-functions defined in a bounded regular domain of
N
. Here we construct families of solutions which blow-up and concentrate at some points in as the positive parameter goes to zero.*The authors are supported by M.I.U.R., project Metodi variazionali e topologici nello studio di fenomeni non lineari. 相似文献
2.
Shuang-jie Peng 《应用数学学报(英文版)》2006,22(1):137-162
Abstract Let Ω be the unit ball centered at the origin in
. We study the following problem
By a constructive argument, we prove that for any k = 1, 2, • • •, if ε is small enough, then the above problem has positive a solution uε concentrating at k distinct points which tending to the boundary of Ω as ε goes to 0+. 相似文献
3.
4.
Sufficient conditions of solvability and unique solvability of the boundary value problem
are established, where
are measurable functions and the vector function
is measurable in the first and continuous in the last kmn arguments; moreover, this function may have nonintegrable singularities with respect to the first argument. 相似文献
5.
Résumé Dans un célèbre papier ([3]), B. GIDAS et J.SPRUCK ont utilisé-sous des hypothèses adéquates- la technique du “blow up” pour
montrer que les solutionsu ∈C
0
∩C
1 (Ω) du problème
admettent une estimation a priori dansC
0
.
Dans ce travail, on montre que, si les solutionsu sont juste supposéesC
0
, une telle estimation a priori n’existe plus.
In a famous paper ([3]), B. GIDAS and J. SPRUCK used a “blow-up” argument to show that, under appropriate assumptions, all
the solutionsu ∈C
0
∩C
1 (Ω) of the problem
admit an a priori estimate inC
0
.
In this work, we show that, if one supposes the solutions are only inC
0
, such an a priori estimate does not hold. 相似文献
6.
Zhi Wen DUAN Kwang Ik KIM 《数学学报(英文版)》2007,23(6):1083-1094
This paper is concerned with a nonlocal hyperbolic system as follows utt = △u + (∫Ωvdx )^p for x∈R^N,t〉0 ,utt = △u + (∫Ωvdx )^q for x∈R^N,t〉0 ,u(x,0)=u0(x),ut(x,0)=u01(x) for x∈R^N,u(x,0)=u0(x),ut(x,0)=u01(x) for x∈R^N, where 1≤ N ≤3, p ≥1, q ≥ 1 and pq 〉 1. Here the initial values are compactly supported and Ω belong to R^N is a bounded open region. The blow-up curve, blow-up rate and profile of the solution are discussed. 相似文献
7.
Let be a bounded domain in #x211D;n with a smooth boundary . In this work we study the existence of solutions for the following boundary value problem:
where M is a C
1-function such that M() 0 > 0 for every 0 and f(y) = |y|
y for 0. 相似文献
8.
Here we study the local or global behaviour of the solutions of elliptic inequalities involving quasilinear operators of the
type
or
. We give integral estimates and nonexistence results. They depend on properties of the supersolutions of the equationsL
A
u=0,L
B
v=0, which suppose weak coercivity conditions. Under stronger conditions, we give pointwise estimates in case of equalities,
using Harnack properties. 相似文献
9.
Wu Shaoping 《数学学报(英文版)》1991,7(1):4-12
LetL be a self-adjoint linear operator andN be the gradient of a functional ϕ, which is almost quadratic. We first give a theorem on the surjectivity of the operatorL+N, then apply the result to semilinear elliptic systems:
相似文献
10.
Given H≥0 and bounded convex curves α1, ...,⇌n, α in the plane z=0 bounding domains D1, …, Dn, D, respectively, with
if i ∈ j and with Di ⊂ D, we obtain several results proving the existence of a constanth depending only on H and on the geometry of the curves
αi, α such that the Dirichlet problem for the constant mean curvature H equation:
where
may accept or not a solution. 相似文献
11.
Yuanji Cheng 《Czechoslovak Mathematical Journal》1997,47(4):681-687
In this paper, we consider the existence and nonexistence of positive solutions of degenerate elliptic systems
where –p is the p-Laplace operator, p > 1 and is a C
1,-domain in
. We prove an analogue of [7, 16] for the eigenvalue problem with
and obtain a non-existence result of positive solutions for the general systems. 相似文献
12.
On Kolmogorov-Type Inequalities Taking into Account the Number of Changes in the Sign of Derivatives
For 2-periodic functions
and arbitrary q [1, ] and p (0, ], we obtain the new exact Kolmogorov-type inequality
which takes into account the number of changes in the sign of the derivatives (x
(k)) over the period. Here, = (r – k + 1/q)/(r + 1/p),
r
is the Euler perfect spline of degree r,
and
. The inequality indicated turns into the equality for functions of the form x(t) = a
r
(nt + b), a, b R, n N. We also obtain an analog of this inequality in the case where k = 0 and q = and prove new exact Bernstein-type inequalities for trigonometric polynomials and splines. 相似文献
13.
具时滞的奇异(n-1,1)共轭边值问题的多重正解 总被引:2,自引:0,他引:2
WengPeixuan TianYanling 《高校应用数学学报(英文版)》2000,15(2):128-136
Abstract. This paper discusses the singular (n-l, 1) conjugate boundary value problem as fol-lows by using a fixed point index theorem in cones 相似文献
14.
Wang Lei Pan Ting Dept. of Math. Zhejiang Univ. Hangzhou China. Univ. of International Relation Hangzhou China. 《高校应用数学学报(英文版)》2004,19(2):212-222
Ibαf ( x) =∫R ∏mj=1( bj( x) - bj( y) ) 1| x - y| n-αf ( y) dyare considered.The following priori estimates are proved.For 1
01Φ1t| {y∈Rn:| Ibαf( y) | >t}| 1q ≤csupt>01Φ1t| {y∈Rn:ML( log L) 1r ,α(‖b‖f ) ( y) >t}| 1q,where‖b‖=∏mj=1‖bj‖Oscexp Lrj,Φ( t) =t( 1 + log+t) 1r,1r =1r1+ ...+ 1rm,ML(… 相似文献 15.
宋仁明 《应用数学学报(英文版)》1989,5(2):137-147
In this paper we provide a probabilistic approach to the following Dirichlet Problem{(∑x~4(α~(ij) x~j) ∑b~ix~i ξ)u=0, iD u=g, on D,without assuming that the eigenvalues of the operator∑x~i(α~(ij)x~j) ∑b~ix~i ξwith Dirichlet boundary conditions are all strictly negative. The results of this paper generalizedthose of Ma. 相似文献
16.
V. Zh. Dumanyan 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2010,45(1):26-42
The paper suggests some conditions on the lower order terms, which provide that the solution of the Dirichlet problem for
the general elliptic equation of the second order
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