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1.
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
2.
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
3.
4.
Comparison theorem and uniqueness of positive solutions for sublinear elliptic equations 总被引:1,自引:0,他引:1
Ryuji Kajikiya 《Archiv der Mathematik》2008,91(5):427-435
In semilinear elliptic equations, we prove that the necessary and sufficient condition for the comparison theorem of positive
solutions to be valid is that the nonlinear term is sublinear. Our theorem needs neither any regularity of the nonlinear term
nor the smoothness of the boundary. Applying this theorem, we prove the uniqueness of positive solutions for the Dirichlet
problem.
Received: 9 April 2008 相似文献
5.
F. Rousset 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2007,58(1):53-67
In this note we study the convergence in the limit of small Ekman and Rossby numbers of the magnetohydrodynamics equations
relevant to describe the flow in the Earth core. In particular, we prove the nonlinear stability of Ekman-Hartmann type boundary
layers in a spherical geometry for some class of well-prepared initial data. 相似文献
6.
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
7.
J. Chabrowski 《Journal of Fixed Point Theory and Applications》2008,4(1):137-150
We establish the existence of a solution to the variational inequality (the obstacle problem) (1.1) which involves the critical
Sobolev exponent. This result is also extended to an obstacle problem with a lower order perturbation.
Dedicated to Professor F. Browder on the occasion of his 80-th birthday 相似文献
8.
Jorge García-Melián 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2009,60(4):594-607
In this paper we consider the boundary blow-up problem Δpu = a(x)uq in a smooth bounded domain Ω of , with u = +∞ on ∂Ω. Here is the well-known p-Laplacian operator with p > 1, q > p − 1, and a(x) is a nonnegative weight function which can be singular on ∂Ω. Our results include existence, uniqueness and exact boundary
behavior of positive solutions.
相似文献
9.
This paper is devoted to solving the inverse boundary problem of the heat diagnostics by the projective regularization method. We obtain exact with respect to the order error estimates of the corresponding approximate solution. 相似文献
10.
Djairo G. de Figueiredo João Marcos do Ó Bernhard Ruf 《Journal of Fixed Point Theory and Applications》2008,4(1):77-96
We establish a priori bounds for positive solutions of semilinear elliptic systems of the form
where Ω is a bounded and smooth domain in . We obtain results concerning such bounds when f and g depend exponentially on u and v. Based on these bounds, existence of positive solutions is proved.
Dedicated to Felix Browder on the occasion of his 80th birthday 相似文献
11.
Pasquale Candito 《Rendiconti del Circolo Matematico di Palermo》2006,55(1):43-52
We use critical point theory to establish the existence of at least two solutions to a nonlinear Neumann problem involving
the one-dimensional p-Laplacian without assuming asymptotic conditions at infinity on the nonlinearity. 相似文献
12.
Exact solutions are derived for the class of two dimensional couple stress flows. This class consists of flows for which the
vorticity distribution is proportional to the stream function perturbed by a uniform stream. The solutions are obtained by
applying the so-called inverse method which makes certain hypothesis a priori on the form of the velocity field and pressure
without making any on the boundaries of the domain occupied by the fluid. Exact solutions are obtained for both steady and
unsteady cases. 相似文献
13.
A. M. Vershik 《Journal of Fixed Point Theory and Applications》2008,3(2):317-329
We consider the sequence of the hyperspheres M
n
, i.e., the homogeneous transitive spaces of the Cartan subgroup of the group and study the normalized limit of the corresponding sequence of invariant measures m
n
on those spaces. In the case of compact groups and homogeneous spaces, for example, for the classical pairs (SO(n), S
n-1), n = 1, 2, … , the limit of the corresponding measures is the classical infinite-dimensional Gaussian measure; this is the well-known
Maxwell-Poincaré lemma. Simultaneously the Gaussian measure is a unique (up to a scalar) invariant measure with respect to
the action of the infinite orthogonal group O(∞). This coincidence implies the asymptotic equivalence between grand and small canonical ensembles for the series of the
pairs (SO(n), S
n-1). Our main result shows that the situation for noncompact groups, for example for the case , is completely different: the limit of the measures m
n
does not exist in the literal sense, and we show that only a normalized logarithmic limit of the Laplace transforms of those
measures does exist. At the same time, there exists a measure which is invariant with respect to a continuous analogue of
the Cartan subgroup of the group GL(∞), the so-called infinite-dimensional Lebesgue measure (see [7]). This difference is an evidence for non-equivalence between
the grand and small canonical ensembles in the noncompact case.
To my friend Dima Arnold 相似文献
14.
LiuHuizhao JiangDaqing 《高校应用数学学报(英文版)》1999,14(1):1-6
By coincidence degree, the existence of solution to the periodic boundary value problem of functional differential equations with perturbation 相似文献
15.
In this paper, we explicitly characterize a class of solutions to the first order quasilinear system of partial differential
equations (PDEs), governing one dimensional unsteady planar and radially symmetric flows of an adiabatic gas involving shock
waves. For this, Lie group analysis is used to identify a finite number of generators that leave the given system of PDEs
invariant. Out of these generators, two commuting generators are constructed involving some arbitrary constants. With the
help of canonical variables associated with these two generators, the assigned system of PDEs is reduced to an autonomous
system, whose simple solutions provide non trivial solutions of the original system. It is interesting to remark that one
of the special solutions obtained here, using this approach, is precisely the blast wave solution known in the literature.
相似文献
16.
Shuichi Sato 《Integral Equations and Operator Theory》2008,62(3):429-440
We prove certain L
p
-estimates for Littlewood-Paley functions arising from rough kernels. The estimates are useful for extrapolation to prove
L
p
-boundedness of the Littlewood-Paley functions under a sharp kernel condition.
相似文献
17.
18.
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
19.
Let 2 ≤ p < 100 be a rational prime and consider equation (3) in the title in integer unknowns x, y, n, k with x > 0, y > 1, n ≥ 3 prime, k ≥ 0 and gcd(x, y) = 1. Under the above conditions we give all solutions of the title equation (see the Theorem). We note that if in (3) gcd(x, y) = 1, our Theorem is an extension of several earlier results [15], [27], [2], [3], [5], [23].
Received: 25 April 2008 相似文献
20.
Antal Járai 《Aequationes Mathematicae》1994,47(1):69-78
In this work it is proved that under certain conditions the continuous vector-valued solutionsf of the functional equation
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