共查询到20条相似文献,搜索用时 15 毫秒
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Rossella Bartolo Anna Maria Candela Addolorata Salvatore 《NoDEA : Nonlinear Differential Equations and Applications》2013,20(5):1701-1721
The aim of this paper is investigating the existence and the multiplicity of weak solutions of the quasilinear elliptic problem $$\left\{\begin{array}{ll}-\Delta_p u\ =\ g(x, u) \quad {\rm in} \quad \Omega,\\ u=0 \qquad \qquad \qquad {\rm on}\quad \partial\Omega,\end{array}\right.$$ where ${1 < p < + \infty, \Delta_p u = {\rm div}(|\nabla {u}|^{p-2}\nabla {u})}$ , Ω is an open bounded domain of ${\mathbb{R}^N (N \geq 3)}$ with smooth boundary ?Ω and the nonlinearity g behaves as u p?1 at infinity. The main tools of the proof are some abstract critical point theorems in Bartolo et al. (Nonlinear Anal. 7: 981–1012, 1983), but extended to Banach spaces, and two sequences of quasi–eigenvalues for the p–Laplacian operator as in Candela and Palmieri (Calc. Var. 34: 495–530, 2009), Li and Zhou (J. Lond. Math. Soc. 65: 123–138, 2002). 相似文献
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《Discrete Applied Mathematics》1988,21(2):101-111
We consider the broadcasting problem for one-dimensional grid graphs with a given neighborhood template. There are two different models that have been considered-shouting (a node informs all of its neighbors in one step) and whispering (a node informs a single neighbor in one step). Let σ(t) (respectively ω(t)) denote the maximum number of nodes that can be reached in t steps by shouting (respectively whispering) broadcast from a single source.We obtain detailed information about the benefits of shouting over whispering. We prove for the one-dimensional case a conjecture by Stout that ω(t) eventually becomes a polynomial. In particular, we show that there exist constants i and t0 such that ω(t)=σ(t)−i for all t ≥ t0. When the broadcast only goes in one direction (i.e., when all elements of the template are positive), we also determine that i=d −1 and t0≤3d for a neighborhood template with the furthest neighbor at distance d. 相似文献
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Both authors were partially supported by grants from the N.S.F. 相似文献
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Jana Bjö rn Stephen Buckley Stephen Keith 《Proceedings of the American Mathematical Society》2006,134(3):703-705
In this note we show that -admissible measures in one dimension (i.e. doubling measures admitting a -Poincaré inequality) are precisely the Muckenhoupt -weights.
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Pavel Drábek Petr Girg Raul Manásevich 《NoDEA : Nonlinear Differential Equations and Applications》2001,8(3):285-298
In this paper we give a generic necessary and sufficient condition for the solvability of? Received November 1999 相似文献
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Peter Gács 《Random Structures and Algorithms》2015,47(3):520-560
Let v, w be infinite 0‐1 sequences, and a positive integer. We say that is ‐embeddable in , if there exists an increasing sequence of integers with , such that , for all . Let and be coin‐tossing sequences. We will show that there is an with the property that is ‐embeddable into with positive probability. This answers a question that was open for a while. The proof generalizes somewhat the hierarchical method of an earlier paper of the author on dependent percolation. © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 47, 520–560, 2015 相似文献
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In this paper, we consider mixed problems with a timelike boundary derivative (or a Dirichlet) condition for semilinear wave equations with exponential nonlinearities in a quarter plane. The case when the boundary vector field is tangent to the characteristic which leaves the domain in the future is also considered. We show that solutions either are global or blow up on a C1 curve which is spacelike except at the point where it meets the boundary; at that point, it is tangent to the characteristic which leaves the domain in the future. 相似文献
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In this paper, we consider mixed problems with a spacelike boundary derivative condition for semilinear wave equations with exponential nonlinearities in a quarter plane. Results similar to those obtained earlier by Caffarelli-Friedman for Cauchy problems and power nonlinearities are proved in the present situation, namely we show that solutions either are global or blow up on a spacelike curve. Weaker results are also obtained if the boundary vector field is tangent to the characteristic which leaves the domain in the future. Received January 7, 2000 / Accepted July 17, 2000 /Published online December 8, 2000 相似文献
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We prove rigidity type results on the vanishing of stable Ext and Tor for modules of finite complete intersection dimension, results which generalize and improve upon known results. We also introduce a notion of pre-rigidity, which generalizes phenomena for modules of finite complete intersection dimension and complexity one. Using this concept, we prove results on length and vanishing of homology modules. 相似文献
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John M Chadam 《Journal of Functional Analysis》1973,13(2):173-184
The existence of global solutions of the Cauchy problem is proved for the Maxwell-Dirac equations coupled through the standard electromagnetic interaction. The proof depends on the conservation of charge and an a priori estimate on the electromagnetic potential. The technique also applies to the Dirac-Klein-Gordon equations with Yukawa coupling. 相似文献
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Let H be the symmetric second-order differential operator on L 2(R) with domain ${C_c^\infty({\bf R})}Let H be the symmetric second-order differential operator on L
2(R) with domain Cc¥(R){C_c^\infty({\bf R})} and action Hj = -(c j¢)¢{H\varphi=-(c\,\varphi^{\prime})^{\prime}} where c ? W1,2loc(R){ c\in W^{1,2}_{\rm loc}({\bf R})} is a real function that is strictly positive on R\{0}{{\bf R}\backslash\{0\}} but with c(0) = 0. We give a complete characterization of the self-adjoint extensions and the submarkovian extensions of H. In particular if n = n+ún-{\nu=\nu_+\vee\nu_-} where n±(x)=±ò±1±x c-1{\nu_\pm(x)=\pm\int^{\pm 1}_{\pm x} c^{-1}} then H has a unique self-adjoint extension if and only if n ? L2(0,1){\nu\not\in L_2(0,1)} and a unique submarkovian extension if and only if n ? L¥(0,1){\nu\not\in L_\infty(0,1)}. In both cases, the corresponding semigroup leaves L
2(0,∞) and L
2(−∞,0) invariant. In addition, we prove that for a general non-negative c ? W1,¥loc(R){ c\in W^{1,\infty}_{\rm loc}({\bf R})} the corresponding operator H has a unique submarkovian extension. 相似文献
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This is one of a series of papers exploring the stability speed of one-dimensional stochastic processes. The present paper emphasizes on the principal eigenvalues of elliptic operators. The eigenvalue is just the best constant in the L 2-Poincaré inequality and describes the decay rate of the corresponding diffusion process. We present some variational formulas for the mixed principal eigenvalues of the operators. As applications of these formulas, we obtain case by case explicit estimates, a criterion for positivity, and an approximating procedure for the eigenvalue. 相似文献
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Evgenia Soprunova 《Proceedings of the American Mathematical Society》2008,136(1):239-245
Gelfond and Khovanskii found a formula for the sum of the values of a Laurent polynomial over the zeros of a system of Laurent polynomials in . We expect that a similar formula holds in the case of exponential sums with real frequencies. Here we prove such a formula in dimension one.
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Geoffrey R. Grimmett Thomas M. Liggett Thomas Richthammer 《Random Structures and Algorithms》2010,37(1):85-99
We consider a type of long‐range percolation problem on the positive integers, motivated by earlier work of others on the appearance of (in)finite words within a site percolation model. The main issue is whether a given infinite binary word appears within an iid Bernoulli sequence at locations that satisfy certain constraints. We settle the issue in some cases, and we provide partial results in others. © 2010 Wiley Periodicals, Inc. Random Struct. Alg., 2010 相似文献