共查询到20条相似文献,搜索用时 828 毫秒
1.
A. P. Scheglova 《Journal of Mathematical Sciences》2005,128(5):3306-3333
We consider the boundary-value problem
where
and n is the unit outward normal. We show that there exist so many nonequivalent positive weak solutions as prescribed under certain conditions on q and R. We construct nonradial solutions for [(n + 1)/2] + 1 ⩽ p < n and some q. Bibliography: 18 titles.__________Translated from Problemy Matematicheskogo Analiza, No. 30, 2005, pp. 121–144. 相似文献
2.
Using measure-capacity inequalities we study new functional inequalities, namely L
q
-Poincaré inequalities
and L
q
-logarithmic Sobolev inequalities
for any q ∈ (0, 1]. As a consequence, we establish the asymptotic behavior of the solutions to the so-called weighted porous media
equation
for m ≥ 1, in terms of L
2-norms and entropies.
相似文献
3.
V. V. Kurta 《Mathematical Notes》1999,65(4):462-469
The main result of the paper is the nonexistence of integer positive solutions in wide classes of quasilinear elliptic equations
whose model examples are equations of the form {
}, where α>1 andq are some fixed real numbers.
Translated fromMatematicheskie Zametki, Vol. 65, No. 4, pp. 552–561, April, 1999. 相似文献
4.
In this paper we consider the bifurcation problem -div A(x, u)=λa(x)|u|^p-2u+f(x,u,λ) in Ω with p 〉 1.Under some proper assumptions on A(x,ξ),a(x) and f(x,u,λ),we show that the existence of an unbounded branch of positive solutions bifurcating Irom the principal eigenvalue of the problem --div A(x, u)=λa(x)|u|^p-2u. 相似文献
5.
Pigong Han 《Israel Journal of Mathematics》2008,164(1):125-152
Let Ω be an open bounded domain in ℝN(N ≥ 3) and
. We are concerned with two kinds of critical elliptic problems. The first one is
where 0 ∈ Ω,
, 2 < m < 2* and λ > 0. By using the fountain theorem and concentration estimates, if N ≥ 7 and θ > 0, we establish the existence of infinitely many solutions for the following regularization of (*) with small number ϵ > 0
Then if θ > 0 is suitably small, we obtain many solutions for problem (*) by taking the process of approximation.
The second problem is
where q ∈ (0, 1), t > 0. By using similar methods as in (*), we prove that if N ≥ 7,
and t > 0, there exist infinitely many solutions with positive energy. In particular, we give a positive answer to one open problem
proposed by Ambrosetti, Brezis and Cerami [1]. 相似文献
(*) |
6.
Yu Xiang LI 《数学学报(英文版)》2006,22(2):545-550
We will show in this paper that if A is very close to 1, then
I(M,λ,m) =supu∈H0^1,n(m),∫m|△↓u|^ndV=1∫Ω(e^αn|u|^n/(n-1)-λm∑k=1|αnun/(n-1)|k/k!)dV
can be attained, where M is a compact-manifold with boundary. This result gives a counter-example to the conjecture of de Figueiredo and Ruf in their paper titled "On an inequality by Trudinger and Moser and related elliptic equations" (Comm. Pure. Appl. Math., 55, 135-152, 2002). 相似文献
7.
L. V. Kritskov 《Mathematical Notes》1999,65(4):454-461
Suppose thatА is a nonnegative self-adjoint extension to {
} of the formal differential operator−Δu+q(x)u with potentialq(x) satisfying the condition {
} or the condition {
} in which the nonnegative function itχ(r) is such that {
}. For each α∈(0, 2], we establish an estimate of the generalized Fourier transforms of an arbitrary function {
} of the form {
} If, in addition, {
}, then, along with this estimate, a similar lower bound is established.
Translated fromMatematicheskie Zametki, Vol. 65, No. 4, pp. 542–551, April, 1999. 相似文献
8.
Antonio DeSimone Hans Knüpfer Felix Otto 《Calculus of Variations and Partial Differential Equations》2006,27(2):233-253
We are interested in thin-film samples in micromagnetism, where the magnetization m is a 2-d unit-length vector field. More precisely we are interested in transition layers which connect two opposite magnetizations, so called Néel walls.We prove stability of the 1-d transition layer under 2-d perturbations. This amounts to the investigation of the following singularly perturbed energy functional:
The topological structure of this two-dimensional problem allows us to use a duality argument to infer the optimal lower bound. The lower bound relies on an ε-perturbation of the following logarithmically failing interpolation inequality
Mathematics Subject Classification (2000) Primary: 49S05, Secondary: 78A30, 78M30 相似文献
9.
Martin Flucher 《Commentarii Mathematici Helvetici》1992,67(1):471-497
We prove that theTrudinger-Moser constant
相似文献
10.
We prove certain local bifurcation results for the mean curvature problem.
11.
P. ��lvarez-Caudevilla V. A. Galaktionov 《NoDEA : Nonlinear Differential Equations and Applications》2011,18(5):483-537
Countable families of global-in-time and blow-up similarity sign-changing patterns of the Cauchy problem for the fourth-order thin film equation (TFE-4)
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