共查询到20条相似文献，搜索用时 515 毫秒
1.
On a Liouville-type theorem and the Fujita blow-up phenomenon 总被引：3，自引：0，他引：3
The main purpose of this paper is to obtain the well-known results of H.Fujita and K.Hayakawa on the nonexistence of nontrivial nonnegative global solutions for the Cauchy problem for the equation
with on the half-space as a consequence of a new Liouville theorem of elliptic type for solutions of () on . This new result is in turn a consequence of other new phenomena established for nonlinear evolution problems. In particular, we prove that the inequality
has no nontrivial solutions on when We also show that the inequality
has no nontrivial nonnegative solutions for , and it has no solutions on bounded below by a positive constant for 1.$">
with on the half-space as a consequence of a new Liouville theorem of elliptic type for solutions of () on . This new result is in turn a consequence of other new phenomena established for nonlinear evolution problems. In particular, we prove that the inequality
has no nontrivial solutions on when We also show that the inequality
has no nontrivial nonnegative solutions for , and it has no solutions on bounded below by a positive constant for 1.$">
2.
Huaning Liu 《Proceedings of the American Mathematical Society》2008,136(4):1193-1203
For integers , , , with , and Dirichlet character , we define a mixed exponential sum where , and denotes the summation over all with . The main purpose of this paper is to study the mean value of and to give a related identity on the mean value of the general Kloosterman sum where .
3.
D. D. Hai 《Proceedings of the American Mathematical Society》2003,131(8):2409-2414
We establish existence and multiplicity of positive solutions to the quasilinear boundary value problem
where is a bounded domain in with smooth boundary , is continuous and p-sublinear at and is a large parameter.
where is a bounded domain in with smooth boundary , is continuous and p-sublinear at and is a large parameter.
4.
The triple integrals
and
where and are complex variables in suitably defined cut planes, were first evaluated by Watson in 1939 for the special cases and , respectively. In the present paper simple direct methods are used to prove that can be expressed in terms of squares of complete elliptic integrals of the first kind for general values of and . It is also shown that and are related by the transformation formula
where
Thus both of Watson's results for are contained within a single formula for .
and
where and are complex variables in suitably defined cut planes, were first evaluated by Watson in 1939 for the special cases and , respectively. In the present paper simple direct methods are used to prove that can be expressed in terms of squares of complete elliptic integrals of the first kind for general values of and . It is also shown that and are related by the transformation formula
where
Thus both of Watson's results for are contained within a single formula for .
5.
Arrigo Cellina 《Proceedings of the American Mathematical Society》2002,130(2):413-418
This paper presents a necessary and sufficient condition on the convex function in order that continuous solutions to
satisfy a Strong Maximum Principle on any open connected .
satisfy a Strong Maximum Principle on any open connected .
6.
Stephen D. Theriault 《Proceedings of the American Mathematical Society》2003,131(9):2953-2962
In proving that the fiber of the double suspension has a classifying space, Gray constructed fibrations
and
He conjectured that is homotopic to the -power map on when is an odd prime. Harper proved this is true when looped once. We remove the loop when . Gray also conjectured that at odd primes factors through a map
We show that this is true as well when .
and
He conjectured that is homotopic to the -power map on when is an odd prime. Harper proved this is true when looped once. We remove the loop when . Gray also conjectured that at odd primes factors through a map
We show that this is true as well when .
7.
Yanick Heurteaux 《Proceedings of the American Mathematical Society》2005,133(9):2711-2720
Consider the function
where 1$"> and is an almost periodic function. It is well known that the function lives in the so-called Zygmund class. We prove that is generically nowhere differentiable. This is the case in particular if the elementary condition is satisfied. We also give a sufficient condition on the Fourier coefficients of which ensures that is nowhere differentiable.
where 1$"> and is an almost periodic function. It is well known that the function lives in the so-called Zygmund class. We prove that is generically nowhere differentiable. This is the case in particular if the elementary condition is satisfied. We also give a sufficient condition on the Fourier coefficients of which ensures that is nowhere differentiable.
8.
David Benko Tamá s Erdé lyi Jó zsef Szabados 《Proceedings of the American Mathematical Society》2003,131(8):2385-2391
For a function defined on an interval let
The principal result of this paper is the following Markov-type inequality for Müntz polynomials. Theorem. Let be an integer. Let be distinct real numbers. Let . Then
where the supremum is taken for all (the span is the linear span over ).
The principal result of this paper is the following Markov-type inequality for Müntz polynomials. Theorem. Let be an integer. Let be distinct real numbers. Let . Then
where the supremum is taken for all (the span is the linear span over ).
9.
Under certain assumptions we show that a wavelet frame
in remains a frame when the dilation matrices and the translation parameters are perturbed. As a special case of our result, we obtain that if is a frame for an expansive matrix and an invertible matrix , then is a frame if and for sufficiently small 0$">.
in remains a frame when the dilation matrices and the translation parameters are perturbed. As a special case of our result, we obtain that if is a frame for an expansive matrix and an invertible matrix , then is a frame if and for sufficiently small 0$">.
10.
Biagio Ricceri 《Proceedings of the American Mathematical Society》2005,133(11):3255-3261
In this paper, we prove the following general result. Let be a real Hilbert space and a continuously Gâteaux differentiable, nonconstant functional, with compact derivative, such that
Then, for each for which the set is not convex and for each convex set dense in , there exist and 0$"> such that the equation
has at least three solutions.
Then, for each for which the set is not convex and for each convex set dense in , there exist and 0$"> such that the equation
has at least three solutions.
11.
S. J. Dilworth Joseph P. Patterson 《Proceedings of the American Mathematical Society》2003,131(5):1489-1500
Let 0$"> be sufficiently small. Then, for , there exists such that if are vectors in the unit ball of a complex Banach space which satisfy
(where are independent complex Steinhaus random variables), then there exists a set , with , such that
for all (). The dependence on of the threshold proportion is sharp.
(where are independent complex Steinhaus random variables), then there exists a set , with , such that
for all (). The dependence on of the threshold proportion is sharp.
12.
Suppose that is an inner map and that . We show that the identity
holds with an abstract boundary value . If the natural compatibility condition is satisfied, then . Here, denotes the image of the surface measure on under . In particular, is inner if and are inner and . Furthermore, we characterize the boundedness of composition operators on Hardy spaces in terms of the absolute continuity of .
13.
Bruce Ebanks 《Proceedings of the American Mathematical Society》2008,136(11):3911-3919
The main result is an improvement of previous results on the equation for a given function . We find its general solution assuming only continuous differentiability and local nonlinearity of . We also provide new results about the more general equation for a given function . Previous uniqueness results required strong regularity assumptions on a particular solution . Here we weaken the assumptions on considerably and find all solutions under slightly stronger regularity assumptions on .
14.
Steve Hofmann 《Proceedings of the American Mathematical Society》2008,136(12):4223-4233
We consider divergence form elliptic operators , defined in , where the coefficient matrix is , uniformly elliptic, complex and -independent. Using recently obtained results concerning the boundedness and invertibility of layer potentials associated to such operators, we show that if in , then for any vector-valued we have the bilinear estimate where and where is the usual non-tangential maximal operator. The result is new even in the case of real symmetric coefficients and generalizes an analogous result of Dahlberg for harmonic functions on Lipschitz graph domains. We also identify the domain of the generator of the Poisson semigroup for the equation in
15.
J. Villadelprat 《Proceedings of the American Mathematical Society》2007,135(8):2555-2565
This paper is devoted to studying the period function of the quadratic reversible centers. In this context the interesting stratum is the family of the so-called Loud's dehomogenized systems, namely We determine several regions in the parameter plane for which the corresponding center has a monotonic period function. To this end we first show that any of these systems can be brought by means of a coordinate transformation to a potential system. Then we apply a monotonicity criterium of R. Schaaf.
16.
E. Ballico 《Proceedings of the American Mathematical Society》2005,133(1):1-10
Let , , be integral varieties. For any integers 0$">, , and set and . Let be the set of all linear -spaces contained in a linear -space spanned by points of , points of , ..., points of . Here we study some cases where has the expected dimension. The case was recently considered by Chiantini and Coppens and we follow their ideas. The two main results of the paper consider cases where each is a surface, more particularly:
or
or
17.
to 
Francine Meylan 《Proceedings of the American Mathematical Society》2006,134(4):1023-1030
Let be a rational proper holomorphic map between the unit ball in and the unit ball in Write where and are holomorphic polynomials, with Recall that the degree of is defined by
deg
In this paper, we give a bound estimate for the degree of improving the bound given by Forstneric (1989). 18.
Petri Huovinen 《Proceedings of the American Mathematical Society》2001,129(11):3345-3351
We construct an example of a purely 1-unrectifiable AD-regular set in the plane such that the limit
exists and is finite for almost every for some class of antisymmetric Calderón-Zygmund kernels. Moreover, the singular integral operators associated with these kernels are bounded in , where has a positive measure.
19.
John R. Akeroyd 《Proceedings of the American Mathematical Society》2002,130(11):3349-3354
Let be a finite, positive Borel measure with support in such that - the closure of the polynomials in - is irreducible and each point in is a bounded point evaluation for . We show that if 0$">and there is a nontrivial subarc of such that
then for each nontrivial closed invariant subspace for the shift on .
-\infty,\end{displaymath}">
then for each nontrivial closed invariant subspace for the shift on .
20.
We prove the existence, uniqueness and Lipschitz regularity of the minima of the integral functional
on ( ) for a class of integrands that are convex in and for boundary data satisfying some barrier conditions. We do not impose regularity or growth assumptions on .
on ( ) for a class of integrands that are convex in and for boundary data satisfying some barrier conditions. We do not impose regularity or growth assumptions on .