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1.
The existence of infinitely many subharmonic solutions is obtained for a class of nonautonomous second order Hamiltonian systems with a new superquadratic condition. Furthermore, we can get the existence of homoclinic solutions as the limit of subharmonics under a stronger superquadratic condition which is still weaker than the growth conditions in the references. 相似文献
2.
By using mountain pass theorem and local link theorem, some existence theorems are obtained for periodic solutions of second order non-autonomous Hamiltonian systems under local superquadratic condition and other suitable conditions. 相似文献
3.
G. Fang 《纯数学与应用数学通讯》1995,48(12):1343-1368
We derive some upper and lower bounds for Morse indices of critical manifolds generated by min-max principles for functionals invariant under a general compact Lie group or a finite group action. The results generalize the similar results in the nonequivariant (no group action) case. In doing so, we also generalize the extension theorem of Dugundji type in the nonequivariant case to the equivariant (group action) case. As an application, we obtain a precise growth estimate for the whole sequence of critical values given by the min-max procedure for some superquadratic second-order differential equations. It is well-known that this growth estimate is crucial in showing the existence of multiple solutions of some superquadratic perturbed Hamiltonian systems and equations. 相似文献
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5.
关于非自治Lagrange系统的周期解 总被引:2,自引:0,他引:2
刘水强 《应用泛函分析学报》2003,5(1):75-78
用变分方法研究非自治Lagrange系统周期解的问题转化为研究Lagrange作用泛函的临界点问题。对Lagrange系统,人们用变分方法已经获得了一系列可解性条件,但是除在超二次条件下,Lagrange作用泛函都是下方有界的。这里的目的是给出Lagrange作用泛函无界的Lagrange系统周期解的其它可解性条件,这时的主要困难是对应的Lagrange作用泛函不再是下方有界的。这里用临界点理论中的鞍点定理得到了Lagrange系统周期解的存在性。 相似文献
6.
This article deals with the existence and the uniqueness of solutions to quadratic and superquadratic Markovian backward stochastic differential equations (BSDEs) with an unbounded terminal condition. Our results are deeply linked with a strong a priori estimate on Z that takes advantage of the Markovian framework. This estimate allows us to prove the existence of a viscosity solution to a semilinear parabolic partial differential equation with nonlinearity having quadratic or superquadratic growth in the gradient of the solution. This estimate also allows us to give explicit convergence rates for time approximation of quadratic or superquadratic Markovian BSDEs. 相似文献
7.
By using the variant fountain theorem, we study the existence of periodic solutions for a class of superquadratic non-autonomous second-order discrete Hamiltonian systems. 相似文献
8.
Some existence theorems are obtained for periodic solutions of a class of non-autonomous second order Hamiltonian systems with local superquadratic potential, by making use of the generalized mountain pass theorem. 相似文献
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10.
In this paper we consider a class of semilinear Schrödinger equation which terms are asymptotically periodic at infinity. Under a weaker superquadratic condition on the nonlinearity, the existence of a ground state solution is established. The main tools employed here to overcome the new difficulties are the concentration-compactness principle and the Local Mountain Pass Theorem. 相似文献
11.
We study Hamilton Jacobi Bellman equations in an infinite dimensional Hilbert space, with Lipschitz coefficients, where the Hamiltonian has superquadratic growth with respect to the derivative of the value function, and the final condition is not bounded. This allows to study stochastic optimal control problems for suitable controlled state equations with unbounded control processes. The results are applied to a controlled wave equation. 相似文献
12.
In this paper, we are concerned with the existence of periodic solutions for a class of damped vibration problems. By introducing some new kinds of superquadratic and asymptotically quadratic conditions, and making use of the generalized mountain pass theorem in critical point theory, we propose a unified approach when the potential function exhibits either an asymptotically quadratic or a superquadratic behavior at infinity, and establish some sufficient conditions on periodic solutions, which extend and improve some recent results in the literature, even without damped vibration term. 相似文献
13.
Yalin Qiu 《Nonlinear Analysis: Theory, Methods & Applications》2012,75(8):3574-3590
We consider the regularity for weak solutions of second order nonlinear elliptic systems with Dini continuous coefficients for the superquadratic case under natural growth condition, and obtain a general criterion for a weak solution to be regular in the neighborhood of a given point. In particular, the proof yields directly the optimal Hölder exponent for the derivative of the weak solutions on the regular set. 相似文献
14.
Zhu-Lian Tao Shang'an Yan Song-Lin Wu 《Journal of Mathematical Analysis and Applications》2007,331(1):152-158
We prove the existence of nontrivial critical points for a class of superquadratic nonautonomous second-order Hamiltonian systems by applying condition ∗(C) to critical point theory, and some new solvability conditions of nontrivial periodic solutions are obtained. 相似文献
15.
The direct method is used to prove the existence of optimalopen-loop controls for stochastic optimal control problems inBolza form. Instead of requiring the control set to be compact,as previous authors have done, we impose a superquadratic growthcondition on the running cost. Degeneracy of the diffusion coefficientis allowed by this approachin fact, the main result reducesto a well known deterministic theorem when the diffusion coefficientis zero. 相似文献
16.
Shoshana Abramovich Josipa Bari? 《Journal of Mathematical Analysis and Applications》2008,344(2):1048-1056
In this paper we use basic properties of superquadratic functions to obtain new inequalities including Fejer's type and Hermite-Hadamard type inequalities. For superquadratic functions which are also convex, we get refinements of known results. 相似文献
17.
THE EXISTENCE OF HOMOCLINIC ORBITS FOR HAMILTONIAN
SYSTEMS WITH THE POTENTIALS CHANGING SIGN 总被引:1,自引:0,他引:1
Fei Guihua 《数学年刊B辑(英文版)》1996,17(4):403-410
§1.IntroductionandMainResults WeconsidertheHamiltoniansystems¨q-L(t)q V′(t,q)=0,(HS)where(t,q)∈R×RN,¨q=d2dt2q,V′(t,q)denotesthegradientofV(t,q)withrespecttoq,andthesymmetricmatrixL(t)isassumedtosatisfy:(L)L(t)∈C(R,RN2)andthereexistsλ>0suchthatL(t)x·xλ|x|2,(t,x)∈R×RN.Weassum… 相似文献
18.
ON THE MINIMAL PERIOD FOR PERIODIC SOLUTION PROBLEM OF NONLINEAR HAMILTONIAN SYSTEMS 总被引:1,自引:0,他引:1
Long Yiming 《数学年刊B辑(英文版)》1997,18(4):481-484
ONTHEMINIMALPERIODFORPERIODICSOLUTIONPROBLEMOFNONLINEARHAMILTONIANSYSTEMS**LONGYIMING*AbstractTheauthorprovesasharperestimate... 相似文献
19.
Elves A. de Barros e Silva 《NoDEA : Nonlinear Differential Equations and Applications》1994,1(4):339-363
In this article, it is considered the existence of nonzero solutions for a semilinear elliptic system. First, the existence of one nonzero solution is obtained by applying a version of the generalized mountain pass theorem. Next, a maximum principle is used to derive the existence of a positive and a negative solution. Finally, the generalized Morse theory is used to provides the exist ence of at least three nonzero solutions when the primitive of the nonlinearity has a superquadratic behaviour at infinity.Research partially supported by CNPq/Brazil. 相似文献
20.
Patricio L. Felmer 《manuscripta mathematica》1990,66(1):359-396
This work is devoted to the study of subharmonic solutions near an equilibrium for certain Hamiltonian systems. We impose
a weak condition on the Floquet exponents of the linearized system, and a superquadratic condition on the higher order term.
This last condition is reduced to the center manifold.
This research was supported in part by the Air Force Office of Scientific Research under Grant AFOSR-87-0202. 相似文献