共查询到20条相似文献，搜索用时 15 毫秒
1.
Adimurthi Jacques Giacomoni 《NoDEA : Nonlinear Differential Equations and Applications》2005,12(1):1-20
This paper deals with the existence and the behaviour of global connected branches of positive solutions of the problem
We consider a function h which is smooth and changes sign. 相似文献
2.
Kyril Tintarev 《Journal of Fixed Point Theory and Applications》2008,4(1):97-106
The paper concerns existence of solutions to the scalar field equation
when the nonlinearity f(s) is of the critical magnitude . A necessary existence condition is that the nonlinearity
f divided by the “critical stem” expression is either a constant or a nonmonotone function. Two sufficient conditions known in the literature are: the nonlinearity has
the form of a critical stem with a positive perturbation (Lions), and the nonlinearity has selfsimilar oscillations ([11]).
Existence in this paper is proved also when the nonlinearity has the form of the stem with a sufficiently small negative perturbation,
of the stem with a negative perturbation of sufficiently fast decay rate (but not pointwise small), or of the stem with a
perturbation with sufficiently large positive part.
Dedicated to Felix Browder on the occasion of his 80-th birthday 相似文献
| ((0.1)) |
3.
Let L(x, v) be a Lagrangian which is convex and superlinear in the velocity variable v, and let H(x, p) be the associated Hamiltonian. Conditions are obtained under which every viscosity solution
of the Hamilton-Jacobi equation
is an action function in the large, i.e.,
for all
Received: 13 June 2003 相似文献
4.
N. M. Ivochkina 《Journal of Fixed Point Theory and Applications》2008,4(1):47-56
We adapt to degenerate m-Hessian evolution equations the notion of m-approximate solutions introduced by N. Trudinger for m-Hessian elliptic equations, and we present close to necessary and sufficient conditions guaranteeing the existence and uniqueness
of such solutions for the first initial boundary value problem.
Dedicated to Professor Felix Browder 相似文献
5.
Jan Jankowski 《Rendiconti del Circolo Matematico di Palermo》2006,55(1):95-102
We show the existence of absolutely continuous extremal solutions to the problemx′(t)=f(t, x)h(t)))+g(t)),x(0)=x
0, whereh is an arbitrary continuous deviated argument. Conditions for the uniqueness of solutions are given.
Research partialy supported by grant UG BW 5100 - 5 - 0143 - 4 相似文献
6.
Sandro Zagatti 《Calculus of Variations and Partial Differential Equations》2008,31(4):511-519
We consider a class of non convex scalar functionals of the form
under standard assumptions of regularity of the solutions of the associated relaxed problem and of local affinity of the bipolar
f
** of f on the set {f
** < f}. We provide an existence theorem, which extends known results to lagrangians depending explicitly on the three variables,
by the introduction of integro-extremal minimizers of the relaxed functional which solve the equation
or the opposite one, almost everywhere and in viscosity sense. 相似文献
7.
Andrey Shishkov Laurent Véron 《Calculus of Variations and Partial Differential Equations》2008,33(3):343-375
We study the limit behaviour of solutions of with initial data k
δ
0 when k → ∞, where h is a positive nondecreasing function and p > 1. If h(r) = r
β
, β > N(p − 1) − 2, we prove that the limit function u
∞ is an explicit very singular solution, while such a solution does not exist if β ≤ N(p − 1) − 2. If lim
inf
r→ 0
r
2 ln (1/h(r)) > 0, u
∞ has a persistent singularity at (0, t) (t ≥ 0). If , u
∞ has a pointwise singularity localized at (0, 0). 相似文献
8.
José Maria Gomes 《Archiv der Mathematik》2007,88(3):269-278
Let Ω be a bounded convex domain in
. We consider constrained minimization problems related to the Euler-Lagrange equation
over classes of functions
(Ω) with convex super level sets. We then search for sufficient conditions ensuring that the minimizer obtained is a classical
solution to the above equation.
Supported by ESF activity “Global and geometrical aspects of nonlinear P.D.E.’s.”
Received: 4 April 2006 相似文献
9.
Karen Yagdjian 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2007,58(4):612-645
This paper analyses the properties of the family of self-similar solutions of the generalized Tricomi equation
in the domain
by considering initial conditions on the functions and their derivatives, posed as the Cauchy problem with homogeneous initial
data. For specific values of the power k ( = 1/2 or = 3/2) and n = 1 this problem has applications in the aerodynamics of airfoils operating in transonic flows of perfect or dense gases,
respectively. An integral transformation is suggested and used to represent the solutions of the Cauchy problem with homogeneous
initial functions in terms of fundamental solutions of the classical wave equation (the case k = 0). Then the Cauchy problem with homogeneous initial functions for the wave equation in
is solved. These results are used to derive estimates of the upper bound for solutions’ size and to obtain the asymptotics
for self-similar solutions of the wave equation and of the Tricomi-type equation in the neighbourhood of their light cones. 相似文献
10.
Dimitri Mugnai 《Calculus of Variations and Partial Differential Equations》2008,32(4):481-497
We show that a semilinear Dirichlet problem in bounded domains of in presence of subcritical exponential nonlinearities has four nontrivial solutions near resonance.
Research supported by the Italian National Project Metodi Variazionali ed Equazioni Differenziali Non Lineari. 相似文献
11.
In this paper, we study a system of elliptic equations by applying the Limit Index Theory. Under some assumptions on nonlinear
part, we can obtain the existence of multiple solutions for the equations.
The research is supported by NNSF of China (10471024) and Fujian Provincial Natural Science Foundation of China (A0410015). 相似文献
12.
Changjiang Zhu Zhian Wang 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2004,55(6):994-1014
In this paper, we study the global existence and the asymptotic behavior of the solutions to the Cauchy problem for the following nonlinear evolution equations with ellipticity and dissipative effects
with initial data
where and are positive constants such that < 1, < (1–). Through constructing a correct function
defined by (2.13) and using the energy method, we show
as
and the solutions decay with exponential rates. The same problem is studied by Tang and Zhao [10] for the case of (±, ±) = (0,0).Received: November 18, 2003 相似文献
| ((E)) |
| ((I)) |
13.
Zhian Wang 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2006,57(3):399-418
We derive the optimal decay rates of solution to the Cauchy problem for a set of nonlinear evolution equations with ellipticity
and dissipative effects
with initial data
where α and ν are positive constants such that α < 1, ν < α(1 − α), which is a special case of (1.1). We show that the solution
to the system decays with the same rate to that of its associated homogenous linearized system. The main results are obtained
by the use of Fourier analysis and interpolation inequality under some suitable restrictions on coefficients α and ν. Moreover,
we discuss the asymptotic behavior of the solution to general system (1.1) at the end.
The research was supported by the F. S. Chia Scholarship of the University of Alberta.
Received: January 27, 2005; revised: April 27, 2005 相似文献
14.
Veronica Felli Emmanuel Hebey Frédéric Robert 《NoDEA : Nonlinear Differential Equations and Applications》2005,12(2):171-213
Given (M,g) a smooth compact Riemannian manifold of dimension n ≥ 5, we consider equations like
where
is a Paneitz-Branson type operator with constant coefficients α and aα, u is required to be positive, and
is critical from the Sobolev viewpoint. We define the energy function Em as the infimum of
over the u’s which are solutions of the above equation. We prove that Em (α ) →+∞ as α →+∞ . In particular, for any Λ > 0, there exists α0 > 0 such that for α ≥ α0, the above equation does not have a solution of energy less than or equal to Λ. 相似文献
15.
Luis Caffarelli Yan Yan Li Louis Nirenberg 《Journal of Fixed Point Theory and Applications》2009,5(2):353-395
We study strong maximum principles for singular solutions of nonlinear elliptic and degenerate elliptic equations of second
order. An application is given on symmetry of positive solutions in a punctured ball using the method of moving planes.
Dedicated to Felix Browder on his 80th birthday 相似文献
16.
Massimo Grossi 《NoDEA : Nonlinear Differential Equations and Applications》2005,12(2):227-241
Let Ω be a smooth bounded domain of
with N ≥ 5. In this paper we prove, for ɛ > 0 small, the nondegeneracy of the solution of the problem
under a nondegeneracy condition on the critical points of the Robin function. Our proof uses different techniques with respect
to other known papers on this topic. 相似文献
17.
Victor Palamodov 《Advances in Applied Clifford Algebras》2009,19(2):417-425
The paper addresses the Levi problem for a system of n Fueter equations in a domain in quaternionic space . This problem relates to various conditions of convexity and pseudoconvexity of the boundary of the domain.
Received: October, 2007, Accepted: February, 2008. 相似文献
18.
We consider parabolic variational inequalities having the strong formulation
where
for some admissible initial datum, V is a separable Banach space with separable dual
is an appropriate monotone operator, and
is a convex,
lower semicontinuous functional. Well-posedness of (1) follows from an explicit construction of the related semigroup
Illustrative applications to free boundary problems and to parabolic problems in Orlicz-Sobolev spaces are given. 相似文献
| ((1)) |
19.
On the multiplicity of periodic solutions of mountain pass type for a class of semilinear PDE’s 总被引：1，自引：0，他引：1
We prove the existence of many mountain pass periodic solutions for a semilinear elliptic PDE on a torus.
The first author was supported by the National Science Foundation grant #0300319 and by the RFBR grant #050101119. The second
author was supported by the NSF grant #MCS-8110556. 相似文献
20.
Anna Maria Candela Giuliana Palmieri 《Calculus of Variations and Partial Differential Equations》2009,34(4):495-530
The aim of this paper is investigating the existence of one or more critical points of a family of functionals which generalizes
the model problem
in the Banach space , being Ω a bounded domain in . In order to use “classical” theorems, a suitable variant of condition (C) is proved and is decomposed according to a “good” sequence of finite dimensional subspaces.
The authors acknowledge the support of M.I.U.R. (research funds ex 40% and 60%). 相似文献