共查询到20条相似文献,搜索用时 68 毫秒
1.
Let a be a quadratic form associated with a Schrödinger operator L=-∇·(A∇)+V on a domain Ω⊂Rd. If a is nonnegative on , then either there is W>0 such that for all , or there is a sequence and a function ?>0 satisfying L?=0 such that a[?k]→0, ?k→? locally uniformly in Ω?{x0}. This dichotomy is equivalent to the dichotomy between L being subcritical resp. critical in Ω. In the latter case, one has an inequality of Poincaré type: there exists W>0 such that for every satisfying there exists a constant C>0 such that for all . 相似文献
2.
Jiong Qi Wu 《Journal of Differential Equations》2007,235(2):510-526
Suppose that β?0 is a constant and that is a continuous function with R+:=(0,∞). This paper investigates N-dimensional singular, quasilinear elliptic equations of the form
3.
Milena Chermisi 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(3):695-703
In Rm×Rn−m, endowed with coordinates X=(x,y), we consider the PDE
4.
Let H?1 be a selfadjoint operator in H, let J be a linear and bounded operator from (D(H1/2),∥H1/2·∥) to Haux and for β>0 let be the nonnegative selfadjoint operator in H satisfying
5.
Farid Madani 《Bulletin des Sciences Mathématiques》2008,132(7):575
Let (Mn,g) be a compact riemannian manifold of dimension n?3. Under some assumptions, we prove that there exists a positive function φ solution of the Yamabe equation
6.
Santiago Cano-Casanova 《Journal of Differential Equations》2008,244(12):3180-3203
This paper shows the existence and the uniqueness of the positive solution ?(t) of the singular boundary value problem
7.
Let Ω be a bounded domain in R2, u+=u if u?0, u+=0 if u<0, u−=u+−u. In this paper we study the existence of solutions to the following problem arising in the study of a simple model of a confined plasma
8.
9.
In this paper we investigate linear three-term recurrence formulae with sequences of integers (T(n))n?0 and (U(n))n?0, which are ultimately periodic modulo m, e.g.
10.
Let K denote a field, and let V denote a vector space over K with finite positive dimension. By a Leonard pair on V we mean an ordered pair of linear transformations A : V → V and A∗ : V → V that satisfy the following two conditions:
- (i)
- There exists a basis for V with respect to which the matrix representing A is irreducible tridiagonal and the matrix representing A∗ is diagonal.
- (ii)
- There exists a basis for V with respect to which the matrix representing A∗ is irreducible tridiagonal and the matrix representing A is diagonal.
11.
Yasuhito Miyamoto 《Journal of Differential Equations》2010,249(8):1853-1870
Let (n?3) be a ball, and let f∈C3. We are concerned with the Neumann problem
12.
Giovanni Anello 《Journal of Differential Equations》2007,234(1):80-90
In this paper we prove that if the potential has a suitable oscillating behavior in any neighborhood of the origin (respectively +∞), then under very mild conditions on the perturbation term g, for every k∈N there exists bk>0 such that
13.
Julián López-Gómez 《Journal of Differential Equations》2006,224(2):385-439
In this paper, we prove some optimal uniqueness results for large solutions of a canonical class of semilinear equations under minimal regularity conditions on the weight function in front of the non-linearity and combine these results with the localization method introduced in [López-Gómez, The boundary blow-up rate of large solutions, J. Differential Equations 195 (2003) 25-45] to prove that any large solution L of Δu=a(x)up, p>1, a>0, must satisfy
14.
Biagio Ricceri 《Nonlinear Analysis: Theory, Methods & Applications》2009,71(9):4151-4157
If X is a real Banach space, we denote by WX the class of all functionals possessing the following property: if {un} is a sequence in X converging weakly to u∈X and lim infn→∞Φ(un)≤Φ(u), then {un} has a subsequence converging strongly to u.In this paper, we prove the following result:Let X be a separable and reflexive real Banach space; an interval; a sequentially weakly lower semicontinuous C1 functional, belonging to WX, bounded on each bounded subset of X and whose derivative admits a continuous inverse on X∗; a C1 functional with compact derivative. Assume that, for each λ∈I, the functional Φ−λJ is coercive and has a strict local, not global minimum, say .Then, for each compact interval [a,b]⊆I for which , there exists r>0 with the following property: for every λ∈[a,b] and every C1 functional with compact derivative, there exists δ>0 such that, for each μ∈[0,δ], the equation
Φ′(x)=λJ′(x)+μΨ′(x) 相似文献
15.
Let Ω⊂RN, N?2, be a bounded domain. We consider the following quasilinear problem depending on a real parameter λ>0:
16.
In this paper, we consider the Brezis-Nirenberg problem in dimension N?4, in the supercritical case. We prove that if the exponent gets close to and if, simultaneously, the bifurcation parameter tends to zero at the appropriate rate, then there are radial solutions which behave like a superposition of bubbles, namely solutions of the form
17.
We study the Cauchy problem for a class of p-evolution operators P(t,x,Dt,Dx) in , with less than coefficients with respect to the time variable.According to Lipschitz, log-lipschitz or Hölder regularity we find well-posedness in Sobolev spaces or in Gevrey classes. 相似文献
18.
Norbert Ortner 《Bulletin des Sciences Mathématiques》2003,127(10):835-843
L. Hörmander's extension of Ásgeirsson's mean value theorem states that if u is a solution of the inhomogeneous ultrahyperbolic equation (Δx−Δy)u=f, , , then
19.
Yasutsugu Fujita 《Journal of Number Theory》2009,129(7):1678-1697
A set {a1,…,am} of m distinct positive integers is called a Diophantine m-tuple if aiaj+1 is a perfect square for all i, j with 1?i<j?m. It is conjectured that if {a,b,c,d} is a Diophantine quadruple with a<b<c<d, then d=d+, where d+=a+b+c+2abc+2rst and , , . In this paper, we show that if {a,b,c,d,e} is a Diophantine quintuple with a<b<c<d<e, then d=d+. 相似文献
20.
We study the degeneration dimension of non-archimedean analytic maps into the complement of hypersurface divisors of smooth projective varieties. We also show that there exist no non-archimedean analytic maps into where Di, 1?i?n, are hypersurfaces of degree at least 2 in general position and intersecting transversally. Moreover, we prove that there exist no non-archimedean analytic maps into when D1, D2 are generic plane curves with degD1+degD2?4. 相似文献