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1.
Using the extension of Krasnoselskii's fixed point theorem in a cone, we prove the existence of at least one positive solution to the nonlinear nth order m-point boundary value problem with dependence on the first order derivative. The associated Green's function for the nth order m-point boundary value problem is given, and growth conditions are imposed on the nonlinear term f which ensures the existence of at least one positive solution. A simple example is presented to illustrate applications of the obtained results. 相似文献
2.
Using the extension of Krasnoselskii's fixed point theorem in a cone, we prove the existence of at least one positive solution to the nonlinear nth order m-point boundary value problem with dependence on the first order derivative. The associated Green's function for the nth order m-point boundary value problem is given, and growth conditions are imposed on the nonlinear term f which ensures the existence of at least one positive solution. A simple example is presented to illustrate applications of the obtained results. 相似文献
3.
IntroductionThestudiesofpositiveradialsolutionsforfollowingsemilinearellipticboundaryvalueproblem(P) Δu(X) +g( |X|)f(u(X) ) =0 , R1<|X|<R2 ,u(X) ||X| =R1 =u(X) ||X| =R2 =0(whereR1>0 ,X ∈Rn,n ≥ 2 )arebeingcontinuedforrecent 2 0yearswithoutinterruption[1- 11],becausetheproblem (P)haswi… 相似文献
4.
姚庆六 《应用数学和力学(英文版)》2002,23(12):1458-1463
IntroductionThenonlineartwo_pointboundaryvalueproblem (BVP)(P) w″(t) +λh(t)ew(t) =0 , 0 ≤t≤ 1 ,w( 0 ) =w( 1 ) =0(λ>0 )hasbeenproposedbyGelfand[1]withh(t) ≡ 1 ,thisisthereasonwhywesaytheproblem (P)isaGelfandmodel.Semilinearproblemsofthistypeariseinavarietyofinterestingapplicatio… 相似文献
5.
Based on the Timoshenko beam theory, the finite-deflection and the axial inertia are taken into account, and the nonlinear partial differential equations for flexural waves in a beam are derived. Using the traveling wave method and integration skills, the nonlinear partial differential equations can be converted into an ordinary differential equation. The qualitative analysis indicates that the corresponding dynamic system has a heteroclinic orbit under a certain condition. An exact periodic solution of the nonlinear wave equation is obtained using the Jacobi elliptic function expansion. When the modulus of the Jacobi elliptic function tends to one in the degenerate case, a shock wave solution is given. The small perturbations are further introduced, arising from the damping and the external load to an original Hamilton system, and the threshold condition of the existence of the transverse heteroclinic point is obtained using Melnikov's method. It is shown that the perturbed system has a chaotic property under the Smale horseshoe transform. 相似文献
6.
7.
SINGULARLY PERTURBED NONLINEAR BOUNDARY VALUE PROBLEM FOR A KIND OF VOLTERRA TYPE FUNCTIONAL DIFFERENTIAL EQUATION 总被引:2,自引:0,他引:2
鲁世平 《应用数学和力学(英文版)》2003,24(12):1441-1449
IntroductionThereweresomeresultsofstudyingonboundaryvalueproblemsforfunctionaldifferentialequation[1~6 ]byemployingthetoplolgicaldegreetheoryandsomefixedpointprinciplesinrecentyears.Buttheworktostudyboundaryvalueproblemsfordelaydifferentialequationwithsmallparameterbymeansofthetheoryofsingularperturbationrarelyappeared[7~11].Thereasonforitisthattheworktoconstructtheuppersolutionandlowersolutionforthecaseofdifferentialequationwithdelayisdifficult.Theauthorhasstudiedakindofboundaryvalueproblem… 相似文献
8.
An optimal utilization problem for a class of renewable resources system is investigated. Firstly, a control problem was proposed by introducing a new. utility function which depends on the harvesting effort and the stock of resources. Secondly, the existence ofoptimal solution for the problem was discussed. Then, using a maximum principle for infinite horizon problem, a nonlinear four-dimensional differential equations system was attained. After a detailed analysis of the unique positive equilibrium solution, the existence of limit cycles for the system is demonstrated. Next a reduced system on the central manifold is carefully derived, which assures the stability of limit cycles. Finally significance of the results in bioeconomics is explained. 相似文献
9.
By using Pontryagin's maximum principle we determine the shape of the lightest compressed rotating rod, stable against buckling. It is shown that the cross-sectional area function is determined from the solution of a nonlinear boundary value problem. A variational principle for this boundary value problem is formulated and a first integral is constructed. The optimal shape of a rod is determined by numerical integration. 相似文献
10.
We treat the Cauchy problem for nonlinear systems of viscoelasticity with a memory term. We study the existence and the time decay of the solution to this nonlinear problem. The kernel of the memory term includes integrable singularity at zero and polynomial decay at infinity. We prove the existence of a global solution for space dimensions n3 and arbitrary quadratic nonlinearities. 相似文献
11.
The self-similar singular solution of the fast diffusion equation with nonlinear gradient absorption terms are studied. By a self-similar transformation, the self-similar solutions satisfy a boundary value problem of nonlinear ordinary differential equation (ODE). Using the shooting arguments, the existence and uniqueness of the solution to the initial data problem of the nonlinear ODE are investigated, and the solutions are classified by the region of the initial data. The necessary and sufficient condition for the existence and uniqueness of self-similar very singular solutions is obtained by investigation of the classification of the solutions. In case of existence, the self-similar singular solution is very singular solution. 相似文献
12.
Luciano Vela-Martínez Juan Carlos Jáuregui-Correa Oscar Manuel González-Brambila Gilberto Herrera-Ruiz Alejandro Lozano-Guzmán 《Nonlinear dynamics》2009,56(4):415-427
Chatter is an instability condition in machining processes characterized by nonlinear behavior, such as the presence of limit
cycles, jump phenomenon, subcritical Hopf and period doubling bifurcations. Although the use of nonlinear techniques has provided
a better understanding of chatter, neither a unifying model nor an exact solution has yet been developed due to the intricacy
of the problem. This work proposes a weakly nonlinear model with square and cubic terms in both structural stiffness and regenerative
terms, to represent self-excited vibrations in machining. An approximate solution is derived by using the method of multiple
scales. In addition, a qualitative analysis of the effect of the nonlinear parameters on the stability of the system is performed.
The structural cubic term gives a better representation of the nonlinear behavior, whereas the square term represents a distant
attractor in the stability chart. Instability due to subcritical Hopf bifurcations is established in terms of the eigenvalues
of the model in normal form. An important contribution of this analysis is the representation of hysteresis in terms of new
lobes within the conventional stability limits, useful in restoring stability. This analysis leads to a further understanding
of the nonlinear behavior of regenerative chatter. 相似文献
13.
In this paper, a necessary condition is first presented for the existence of limit cycles in nonlinear systems, then four
theorems are presented for the stability, instability, and semistabilities of limit cycles in second order nonlinear systems.
Necessary and sufficient conditions are given in terms of the signs of first and second derivatives of a continuously differentiable
positive function at the vicinity of the limit cycle. Two examples considering nonlinear systems with familiar limit cycles
are presented to illustrate the theorems. 相似文献
14.
A PREDICT-CORRECT NUMERICAL INTEGRATION SCHEME FOR SOLVING NONLINEAR DYNAMIC EQUATIONS 总被引:1,自引:0,他引:1
A new numerical integration scheme incorporating a predict-correct algorithm forsolving the nonlinear dynamic systems was proposed in this paper. A nonlinear dynamic systemgoverned by the equation v=F(v,t) was transformed into the form as v=Hv f(v,t). Thenonlinear part f(v,t) was then expanded by Taylor series and only the first-order term retained inthe polynomial. Utilizing the theory of linear differential equation and the precise time-integrationmethod, an exact solution for linearizing equation was obtained. In order to find the solution of theoriginal system, a third-order interpolation polynomial of v was used and an equivalent nonlinearordinary differential equation was regenerated. With a predicted solution as an initial value andan iteration scheme, a corrected result was achieved. Since the error caused by linearization couldbe eliminated in the correction process, the accuracy of calculation was improved greatly. Threeengineering scenarios were used to assess the accuracy and reliability of the proposed method andthe results were satisfactory. 相似文献
15.
《Comptes Rendus de l'Académie des Sciences》2001,329(3):169-174
We study the initial-boundary value problem for a system of quasilinear equations of one-dimensional nonlinear thermoviscoelasticity with rapidly oscillating nonsmooth coefficients and initial data. We rigorously justify the passage to the corresponding limit initial-boundary value problem for a system of two-scale homogenized integro-differential equations, including the existence theorem for the limit problem. The results are global with respect to the time interval and the data. 相似文献
16.
The existence of solutions for the 2n-order m-point boundary value problem at resonance is obtained by using the coincidence degree theory of Mawhin.We give an example to demonstrate our result.The interest is that the nonlinear term may be noncontinuous. 相似文献
17.
The interaction between a viscous fluid and an elastic solid is modeled by a system of parabolic and hyperbolic equations,
coupled to one another along the moving material interface through the continuity of the velocity and traction vectors. We
prove the existence and uniqueness (locally in time) of strong solutions in Sobolev spaces for quasilinear elastodynamics
coupled to the incompressible Navier-Stokes equations. Unlike our approach in [5] for the case of linear elastodynamics, we
cannot employ a fixed-point argument on the nonlinear system itself, and are instead forced to regularize it by a particular parabolic artificial viscosity term. We proceed to show that with this specific regularization, we obtain a time interval
of existence which is independent of the artificial viscosity; together with a priori estimates, we identify the global solution
(in both phases), as well as the interface motion, as a weak limit in strong norms of our sequence of regularized problems. 相似文献
18.
陈育森 《应用数学和力学(英文版)》2000,21(2):227-236
Weconsiderinthispaperthesingularperturbationofsecond_ordernonlinearsysteminvolvingintergraloperatorεy″=f(t,y,Ty,ε)y′ g(t,y,Ty,ε),(1)withboundaryperturbationy(t,ε)|t=φ(ε)=α(ε),y(t,ε)|t=1 ψ(ε)=β(ε),(2)whereε>0isasmallparameter,andφ(ε),ψ(ε)areboth,withrespecttoε,sufficientlysmo… 相似文献
19.
Limit Cycle Oscillation and Orbital Stability in Aeroelastic Systems with Torsional Nonlinearity 总被引:6,自引:0,他引:6
The paper treats the question of the existence of limit cycleoscillations of prototypical aeroelastic wing sections with structuralnonlinearity using the describing function method. The chosen dynamicmodel describes the nonlinear plunge and pitch motion of a wing. Themodel includes an asymmetric structural nonlinearity in the pitchdegree-of-freedom. The dual-input describing functions of thenonlinearity are derived for the limit cycle analysis. Analyticalexpressions for the average value, and the amplitude and frequency ofoscillation of pitch and plunge responses are obtained. Based on ananalytical approach as well as the Nyquist criterion, stability of thelimit cycles is examined. Numerical results are presented for a set ofvalues of the flow velocities and the locations of the elastic axiswhich show that the predicted limit cycle oscillation amplitude andfrequency as well as the mean value are quite close to the actualvalues. Furthermore, for the chosen model with linear aerodynamics, itis seen that the amplitude of the pitch limit cycle oscillation does notalways increase with the flow velocity for certain elastic axislocations. 相似文献
20.
We establish a condition for the existence and uniqueness of a periodic solution of a system of nonlinear integro-differential
equations with pulse action. The solution is represented as the limit of periodic iterations. We give estimates for the rate
of convergence and for the exact solution of the system.
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Translated from Neliniini Kolyvannya, Vol. 8, No. 4, pp. 553–573, October–December, 2005. 相似文献