共查询到20条相似文献,搜索用时 0 毫秒
1.
In this paper, we establish sharp two-sided estimates for the Green functions of relativistic stable processes (i.e. Green functions for non-local operators m−(m2/α−Δ)α/2) in half-space-like C1,1 open sets. The estimates are uniform in m∈(0,M] for each fixed M∈(0,∞). When m↓0, our estimates reduce to the sharp Green function estimates for −(−Δ)α/2 in such kind of open sets that were obtained recently in Chen and Tokle [12]. As a tool for proving our Green function estimates, we show that a boundary Harnack principle for Xm, which is uniform for all m∈(0,∞), holds for a large class of non-smooth open sets. 相似文献
2.
A finite volume method for solving Navier-Stokes problems 总被引:1,自引:0,他引:1
Lin Mu 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(17):6686-6695
We develop a finite volume method for solving the Navier-Stokes equations on a triangular mesh. We prove that the unique solution of the finite volume method converges to the true solution with optimal order for velocity and for pressure in discrete H1 norm and L2 norm respectively. 相似文献
3.
A. Salvatore 《Journal of Differential Equations》2008,244(10):2529-2544
We prove the existence of infinitely many solutions for symmetric elliptic systems with nonlinearities of arbitrary growth. Moreover, if the symmetry of the problem is broken by a small enough perturbation term, we find at least three solutions. The proofs utilise a variational setting given by de Figueiredo and Ruf in order to prove an existence's result and the “algebraic” approach based on the Pohozaev's fibering method. 相似文献
4.
For α∈R, let pR(t,x,x) denote the diagonal of the transition density of the α-Bessel process in (0,1], killed at 0 and reflected at 1. As a function of x, if either α≥3 or α=1, then for t>0, the diagonal is nondecreasing. This monotonicity property fails if 1≠α<3. 相似文献
5.
Yehuda Pinchover Achilles Tertikas Kyril Tintarev 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2008
In this paper we prove a sufficient condition, in terms of the behavior of a ground state of a singular p -Laplacian problem with a potential term, such that a nonzero subsolution of another such problem is also a ground state. Unlike in the linear case (p=2), this condition involves comparison of both the functions and of their gradients. 相似文献
6.
In this paper we present a one dimensional and radial theory for the existence of eigenvalues and eigenfunctions for fully nonlinear elliptic (α+1)-homogeneous operators, α>−1. A general theory for the first eigenvalue and eigenfunction exists in the frame of viscosity solutions, but in this particular case a simpler theory can be established, that extends, via degree theory, to obtain the complete set of eigenvalues and eigenfunctions characterized by the number of zeros. 相似文献
7.
Rolando Cavazos-Cadena Daniel Hernández-Hernández 《Nonlinear Analysis: Theory, Methods & Applications》2012
Given a monotone and homogeneous self-mapping f of the n-dimensional positive cone, a family of contractive mappings is used to define an equivalence relation in the index set, as well as a total order among the equivalence classes. Then, it is shown (i) that the cycle times are well-defined at each index belonging to the maximal and minimal classes, and (ii) that the cycle times of f exist at every index whenever a weak convexity condition is satisfied. 相似文献
8.
Using a recent result of Ricceri [10] we prove a multiplicity result for a class of quasilinear eigenvalue problems with nonlinear
boundary conditions on an unbounded domain. Our paper completes previous results obtained by Carstea and Rădulescu [4], Chabrowski
[1], [2], Kandilakis and Lyberopoulos [6] and Pflüger [7].
Received: 17 April 2007 相似文献
9.
Denis Borisov 《Journal of Differential Equations》2009,247(11):3028-1127
We determine the general form of the asymptotics for Dirichlet eigenvalues of the one-dimensional linear damped wave operator. As a consequence, we obtain that given a spectrum corresponding to a constant damping term this determines the damping term in a unique fashion. We also derive a trace formula for this problem. 相似文献
10.
Everaldo Medeiros Kyril Tintarev 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(5):2170-2177
We establish some multiplicity results for a class of boundary value problems involving the Hardy-Sobolev operator using Morse theory. 相似文献
11.
Brigitte E. Breckner Dušan Repovš 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(9):2980-2990
We apply a recently obtained three-critical-point theorem of B. Ricceri to prove the existence of at least three solutions of certain two-parameter Dirichlet problems defined on the Sierpinski gasket. We also show the existence of at least three nonzero solutions of certain perturbed two-parameter Dirichlet problems on the Sierpinski gasket, using both the mountain pass theorem of Ambrosetti and Rabinowitz and that of Pucci and Serrin. 相似文献
12.
Zongming Guo 《Journal of Differential Equations》2005,211(1):187-217
The structure of positive boundary blow-up solutions to quasi-linear elliptic problems of the form −Δpu=λf(u), u=∞ on ∂Ω, 1<p<∞, is studied in a bounded smooth domain , for a class of nonlinearities f∈C1((0,∞)?{z2})∩C0[0,∞) satisfying f(0)=f(z1)=f(z2)=0 with 0<z1<z2, f<0 in (0,z1)∪(z2,∞), f>0 in (z1,z2). Large, small and intermediate solutions are obtained for λ sufficiently large. It is known from Part I (see Structure of boundary blow-up solutions for quasilinear elliptic problems, part (I): large and small solutions, preprint), that the large solution is the unique large solution to the problem. We will see that the small solution is also the unique small solution to the problem while there are infinitely many intermediate solutions. Our results are new even for the case p=2. 相似文献
13.
Pier Domenico Lamberti 《Journal of Differential Equations》2005,216(1):109-133
Let Ω be an open connected subset of Rn of finite measure for which the Poincaré-Wirtinger inequality holds. We consider the Neumann eigenvalue problem for the Laplace operator in the open subset φ(Ω) of Rn, where φ is a locally Lipschitz continuous homeomorphism of Ω onto φ(Ω). Then, we show Lipschitz-type inequalities for the reciprocals of the eigenvalues delivered by the Rayleigh quotient. Then, we further assume that the imbedding of the Sobolev space W1,2(Ω) into the space L2(Ω) is compact, and we prove the same type of inequalities for the projections onto the eigenspaces upon variation of φ. 相似文献
14.
This paper provides a new fixed point theorem for increasing self-mappings G:B→B of a closed ball B⊂X, where X is a Banach semilattice which is reflexive or has a weakly fully regular order cone X+. By means of this fixed point theorem, we are able to establish existence results of elliptic problems with lack of compactness. 相似文献
15.
We obtain nontrivial solutions of a class of nonlocal quasilinear elliptic boundary value problems using the Yang index and critical groups. 相似文献
16.
Foias C. Frazho A. E. Gohberg I. Kaashoek M. A. 《Integral Equations and Operator Theory》1997,28(2):158-190
This paper contains a generalization of the commutant lifting theorem to a time-variant setting. The main result, which is called the three chains completion theorem, is used to solve various nonstationary norm constrained interpolation problems. 相似文献
17.
We prove the existence of multiple constant-sign and sign-changing solutions for a nonlinear elliptic eigenvalue problem under Dirichlet boundary condition involving the p-Laplacian. More precisely, we establish the existence of a positive solution, of a negative solution, and of a nontrivial sign-changing solution when the eigenvalue parameter λ is greater than the second eigenvalue λ2 of the negative p-Laplacian, extending results by Ambrosetti–Lupo, Ambrosetti–Mancini, and Struwe. Our approach relies on a combined use of variational and topological tools (such as, e.g., critical points, Mountain-Pass theorem, second deformation lemma, variational characterization of the first and second eigenvalue of the p-Laplacian) and comparison arguments for nonlinear differential inequalities. In particular, the existence of extremal nontrivial constant-sign solutions plays an important role in the proof of sign-changing solutions. 相似文献
18.
The goal of this note is to provide a new embedding theorem and to derive from this embedding the CLR-type inequality for a potential belonging to a proper subspace of integrable functions. 相似文献
19.
In this paper we consider equilibrium problems in vector metric spaces where the function f and the set K are perturbed by the parameters ε,η. We study the stability of the solutions, providing some results in the peculiar framework of generalized monotone functions, first in the particular case where K is fixed, then under both data perturbation. 相似文献
20.
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