共查询到20条相似文献,搜索用时 78 毫秒
1.
In this paper, under an improved Hardy-Rellich's inequality, we study the existence of multiple and sign-changing solutions for a biharmonic equation in unbounded domain by the minimax method and linking theorem. 相似文献
2.
Adimurthi Stathis Filippas Achilles Tertikas 《Nonlinear Analysis: Theory, Methods & Applications》2009
We obtain the sharp constant for the Hardy-Sobolev inequality involving the distance to the origin. This inequality is equivalent to a limiting Caffarelli–Kohn–Nirenberg inequality. In three dimensions, in certain cases the sharp constant coincides with the best Sobolev constant. 相似文献
3.
Dongsheng Kang 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(2):682-688
In this paper, a kind of quasilinear elliptic problem is studied, which involves the critical exponent and singular potentials. By the Caffarelli-Kohn-Nirenberg inequality and variational methods, some important properties of the positive solution to the problem are established. 相似文献
4.
Antonio Iannizzotto Nikolaos S. Papageorgiou 《Nonlinear Analysis: Theory, Methods & Applications》2009
In this paper we consider a nonlinear Neumann problem driven by the p-Laplacian with a nonsmooth potential (hemivariational inequality). Using minimax methods based on the nonsmooth critical point theory together with suitable truncation techniques, we show that the problem has at least three nontrivial smooth solutions. Two of these solutions have constant sign (one is positive, the other negative). 相似文献
5.
A weighted norm inequality of Muckenhoupt–Wheeden type is obtained for gradients of solutions to a class of quasilinear equations with measure data on Reifenberg flat domains. This essentially leads to a resolution of an existence problem for quasilinear Riccati type equations with a gradient source term of arbitrary power law growth. 相似文献
6.
J. Chabrowski M. Willem 《Calculus of Variations and Partial Differential Equations》2002,15(4):421-431
We investigate the effect of the coefficient of the critical nonlinearity for the Neumann problem on the existence of least
energy solutions. As a by-product we establish a Sobolev inequality with interior norm.
Received: 26 April 2000 / Accepted: 25 February 2001 / Published online: 5 September 2002 相似文献
7.
We prove a Harnack inequality and regularity for solutions of a quasilinear strongly degenerate elliptic equation. We assume the coefficients of the structure conditions to belong to suitable Stummel–Kato classes. 相似文献
8.
A Rayleigh-Faber-Krahn type inequality is used to
derive bounds for boundary value problems appearing in
reaction-diffusion problems where the reactant is consumed.
Interesting quantities are the minimum of the solution and the
measure of the set where it vanishes. The proofs are rather
elementary and apply to problems possessing solutions in a weak
sense. 相似文献
9.
On the sharp constant for the weighted Trudinger–Moser type inequality of the scaling invariant form
Michinori Ishiwata Makoto Nakamura Hidemitsu Wadade 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2014
In this article, we establish the weighted Trudinger–Moser inequality of the scaling invariant form including its best constant and prove the existence of a maximizer for the associated variational problem. The non-singular case was treated by Adachi and Tanaka (1999) [1] and the existence of a maximizer is a new result even for the non-singular case. We also discuss the relation between the best constants of the weighted Trudinger–Moser inequality and the Caffarelli–Kohn–Nirenberg inequality in the asymptotic sense. 相似文献
10.
We extend two Sobolev type inequalities for balls to arbitrary smooth bounded domains. In the case of balls, one inequality is due to Brezis and Lieb and another is due to Escobar. The extension has been achieved by analyzing the asymptotic behaviour of solutions of certain semilinear Neumann problems. 相似文献
11.
A gradient-entropy inequality is established for elliptic diffusion semigroups on arbitrary complete Riemannian manifolds. As applications, a global Harnack inequality with power and a heat kernel estimate are derived. 相似文献
12.
Shihui Zhu Jian ZhangHan Yang 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(17):6244-6255
This paper is concerned with the Cauchy problem for the biharmonic nonlinear Schrödinger equation with L2-super-critical nonlinearity. By establishing the profile decomposition of bounded sequences in H2(RN), the best constant of a Gagliardo-Nirenberg inequality is obtained. Moreover, a sufficient condition for the global existence of the solution to the biharmonic nonlinear Schrödinger equation is given. 相似文献
13.
Through a new powerful potential-theoretic analysis, this paper is devoted to discovering the geometrically equivalent isocapacity forms of Chou–Wang's Sobolev type inequality and Tian–Wang's Moser–Trudinger type inequality for the fully nonlinear 1≤k≤n/2 Hessian operators. 相似文献
14.
It is shown that a special case of the well-known Lojasiewicz gradient inequality is sufficient to give a unified background
for many convergence results in gradient or gradient-like systems appearing previously in the Literature. Besides as an illustration
we give a direct proof of convergence in the case of 1D wave equations by a suitable adaptation of Zelenyak’s method. 相似文献
15.
We prove an optimal logarithmic Sobolev inequality in . Explicit minimizers are given. This result is connected with best constants of a special class of Gagliardo-Nirenberg-type inequalities. 相似文献
16.
In this paper, we study strict feasibility of a bifunction variational inequality. It is proved that a monotone bifunction variational inequality has a nonempty and bounded solution set if and only if it is strictly feasible. Stable solvability of the bifunction variational inequality is discussed under strict feasibility assumption when the domain set is perturbed. Our results generalize earlier results on the classical variational inequality to the case of the bifunction variational inequality. 相似文献
17.
The Adimurthi–Druet [1] inequality is an improvement of the standard Moser–Trudinger inequality by adding a -type perturbation, quantified by , where is the first Dirichlet eigenvalue of Δ on a smooth bounded domain. It is known [3], [10], [14], [19] that this inequality admits extremal functions, when the perturbation parameter α is small. By contrast, we prove here that the Adimurthi–Druet inequality does not admit any extremal, when the perturbation parameter α approaches . Our result is based on sharp expansions of the Dirichlet energy for blowing sequences of solutions of the corresponding Euler–Lagrange equation, which take into account the fact that the problem becomes singular as . 相似文献
18.
Guoqing Zhang Shoudong ManWeiguo Zhang 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(14):4771-4784
In this paper, the eigenvalue problem for a class of quasilinear elliptic equations involving critical potential and indefinite weights is investigated. We obtain the simplicity, strict monotonicity and isolation of the first eigenvalue λ1. Furthermore, because of the isolation of λ1, we prove the existence of the second eigenvalue λ2. Then, using the Trudinger-Moser inequality, we obtain the existence of a nontrivial weak solution for a class of quasilinear elliptic equations involving critical singularity and indefinite weights in the case of 0<λ<λ1 by the Mountain Pass Lemma, and in the case of λ1≤λ<λ2 by the Linking Argument Theorem. 相似文献
19.
We investigate the sharp constants in a Brézis-Gallouët-Wainger type inequality with a double logarithmic term in the Hölder space in a bounded domain in Rn. Ibrahim, Majdoub and Masmoudi gave the sharp constant in the two-dimensional case. We make precise estimates to give the sharp constants, and pass to the case of higher dimensions n≥2. We can also show that the inequality with fixed constants including the sharp ones admits an extremal function under a suitable condition when the domain is a ball. 相似文献
20.
We consider second order linear degenerate elliptic operators which are elliptic with respect to horizontal directions generating a stratified algebra of H-type. Extending a result by Gutiérrez and Tournier (2011) for the Heisenberg group, we prove a critical density estimate by assuming a condition of Cordes–Landis type. We then deduce an invariant Harnack inequality for the non-negative solutions from a result by Di Fazio, Gutiérrez, and Lanconelli (2008). 相似文献