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 共查询到20条相似文献，搜索用时 15 毫秒
1.
The solvability of the nonlocal boundary value problem
in a class of functions is investigated for a quasilinear parabolic equation. The solution uniqueness follows from the maximum principle.  相似文献   

2.
It is shown that the following three limits
  相似文献   

3.
In this paper, I propose some problems, of topological nature, on the energy functional associated to the Dirichlet problem $$\left\{ \begin{gathered} - \Delta {\kern 1pt} {\kern 1pt} u = f\left( {x,u} \right){\text{in}}\Omega \hfill \\ u_{\left| {\wp \Omega } \right.} = 0 \hfill \\ \end{gathered} \right.$$ Positive answers to these problems would produce innovative multiplicity results on problem (Pf).  相似文献   

4.
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   

5.
The paper deals with the system
where and are -matrix functions; is a boundary control; is the solution. The singularities of the fundamental solution corresponding to the controls ( is the Dirac -function) are under investigation. In the case of , the singularities of the fundamental solution are described in terms of the standard scale . In the presence of points an interesting effect occurs: singularities of intermediate (fractional) orders appear. Bibliography: 1 title.  相似文献   

6.
The purpose of this paper is to obtain oscillation criteria for the differential system
  相似文献   

7.
Let r k(n) denote the number of representations of an integer n as a sum of k squares. We prove that
where
Here n = 2 p p p is the prime factorisation of n, n is the square-free part of n, the products are taken over the odd primes p, and ( ) is the Legendre symbol.Some similar formulas for r 7(n) and r 9(n) are also proved.  相似文献   

8.
Two results on composed functions are proven. First we give conditions on and so that the mean behaves like , if , including the examples
1$$ " align="middle" border="0"> , not an integer for . Secondly we find conditions on the real positive numbers , such that are almost periodic and we compute their mean values and spectra.  相似文献   

9.
This paper deals with the existence and the behaviour of global connected branches of positive solutions of the problem
We consider a function h which is smooth and changes sign.  相似文献   

10.
We prove existence and asymptotic behaviour of a weak solutions of a mixed problem for where A is the pseudo-Laplacian operator.  相似文献   

11.
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   

12.
The initial boundary value problem
$ {*{20}{c}} {\rho {u_{tt}} - {{\left( {\Gamma {u_x}} \right)}_x} + A{u_x} + Bu = 0,} \hfill & {x > 0,\quad 0 < t < T,} \hfill \\ {u\left| {_{t = 0}} \right. = {u_t}\left| {_{t = 0}} \right. = 0,} \hfill & {x \geq 0,} \hfill \\ {u\left| {_{x = 0}} \right. = f,} \hfill & {0 \leq t \leq T,} \hfill \\ $ \begin{array}{*{20}{c}} {\rho {u_{tt}} - {{\left( {\Gamma {u_x}} \right)}_x} + A{u_x} + Bu = 0,} \hfill & {x > 0,\quad 0 < t < T,} \hfill \\ {u\left| {_{t = 0}} \right. = {u_t}\left| {_{t = 0}} \right. = 0,} \hfill & {x \geq 0,} \hfill \\ {u\left| {_{x = 0}} \right. = f,} \hfill & {0 \leq t \leq T,} \hfill \\ \end{array}  相似文献   

13.
We consider the first-order Cauchy problem
$ \begin{gathered} \partial _z u + a(z,x,D_x )u = 0,0 < z \leqslant Z, \hfill \\ u|_{z = 0} = u_0 , \hfill \\ \end{gathered} $ \begin{gathered} \partial _z u + a(z,x,D_x )u = 0,0 < z \leqslant Z, \hfill \\ u|_{z = 0} = u_0 , \hfill \\ \end{gathered}   相似文献   

14.
Let u and solve the problem
where is an open set in 0\} ,n \geqslant 2,H = \Delta - \partial _t \hfill \\ \hfill \\ \end{gathered} $$ " align="middle" border="0"> is the heat operator, denotes the characteristic function of , is the unit cylinder in n+1, , and the first equation is satisfied in the sense of distributions. We obtain the optimal regularity of the function u, i.e., we show that . Bibliography: 6 titles.  相似文献   

15.
In this note we correct a mistake in K-Theory 10 (1996), 49–72. In that paper we asserted that under bootstrap hypotheses the short exact sequence
which arises in the computation ofKK(A,B) (is a split sequence. This is not always the case. ThusKK(A,B) (decomposes into the three components
and
However, this is a decomposition in the sense of composition series, not as three direct summands. The same correction applies to the Milnor sequence. If there is no primepfor which bothK(A) (andK(B) *haveptorsion then the decomposition is indeed as direct summands. The other results of the paper are unaffected.  相似文献   

16.
In this paper we consider the existence and asymptotic behavior of solutions of the following problem:
where q>1, q1, >0, >0, 0, is the Laplacian in .  相似文献   

17.
Rhouma  N. Belhaj  Mosbah  M. 《Potential Analysis》2004,21(2):137-150
In this paper, we consider a problem of the form
where d3, f is a positive locally Lipschitz bounded function and g is assumed to change sign. We give some conditions of integral type to get the existence of positive solutions for large enough.  相似文献   

18.
The authors consider the finite volume approximation of a reaction-diffusion system with fast reversible reaction.It is deduced from a priori estimates that the approximate solution converges to the weak solution of the reaction-diffusion problem and satisfies estimates which do not depend on the kinetic rate.It follows that the solution converges to the solution of a nonlinear diffusion problem,as the size of the volume elements and the time steps converge to zero while the kinetic rate tends to infinity.  相似文献   

19.
The authors study the existence of nontrivial solutions to p-Laplacian variational inclusion systems
$\left\{ \begin{gathered} - \Delta _p u + \left| u \right|^{p - 2} u \in \partial _1 F\left( {u,v} \right), in \mathbb{R}^N , \hfill \\ - \Delta _p v + \left| v \right|^{p - 2} v \in \partial _2 F\left( {u,v} \right), in \mathbb{R}^N , \hfill \\ \end{gathered} \right.$\left\{ \begin{gathered} - \Delta _p u + \left| u \right|^{p - 2} u \in \partial _1 F\left( {u,v} \right), in \mathbb{R}^N , \hfill \\ - \Delta _p v + \left| v \right|^{p - 2} v \in \partial _2 F\left( {u,v} \right), in \mathbb{R}^N , \hfill \\ \end{gathered} \right.  相似文献   

20.
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