[PDF] Top 20 Boundedness of solutions for semilinear Duffing’s equation with asymmetric nonlinear term

... The first positive result of boundedness of solutions in the superlinear case (i.e., g(x,t) x → ∞ as |x| → ∞) was due to Morris []. By means of KAM theorem, Morris proved that every solution of differential ... See full document

... nonexistence, uniqueness and asymptotic behavior of large solutions to Eq. (1.1) have been investigated extensively by many authors in different contexts. When Ω is a bounded domain, a “large solution” is ... See full document

... quasi-periodic solutions for (.). This equation models the motion of a particle subject to an asymmetric restoring force (see ...quasi-periodic solutions in generalized sense, that is, the ... See full document

... of solutions for a variety of generalizations of such models have subsequently been investigated in a number of previous works, ...of semilinear parabolic equation involving memory terms in a re- ... See full document

... Rao equation and The Chen-Lee-Lin equation to Duffing oscillator [7] and derived the periodic solutions with the aid of the homogenous balance ...obtained equation (1) from extended ... See full document

... studies of Duffing in 1918 1, has a cubic nonlinearity, and describes an oscillator. It is the simplest oscillator displaying catastrophic jumps of amplitude and phase when the frequency of the forcing term is taken ... See full document

... the solutions to be ...bounded solutions of linear Volterra difference equations with infinite delay and its ...bounded solutions of a linear Volterra difference equation with unbounded delay ... See full document

... The Duffing equation is a mathematical representation of the ...the equation and oscillator are prone to many output ...The Duffing equation can be a forced or unforced damped chaotic ... See full document

... all solutions of a time-scale first-order nonlinear vari- able-delay dynamic equation with forcing term are bounded and vanish at infinity, for arbitrary time scales that are unbounded ... See full document

... perturbation term f(t, x) satisfying some suitable growth conditions, can be allowed to be either a bounded function or an unbounded function, which differs from many existing results in the ... See full document

... several solutions valid inside consecutive subintervals of the main ...corresponding solutions must be done in each point that solution changes in order to ensure the appropriate ... See full document

... and boundedness of solutions of equa- tion () have not yet been discussed in the ...and boundedness of solutions of equation ...of solutions of functional integro-differential ... See full document

... coupled in the first equation. Motivated by the above works, we are devoted to study problem (1.1). By virtue of the potential well method, and through Galerkin procedures, we acquire the global existence and ... See full document

... Wang [42] considered problem (1.1)-(1.2) but with a linear damping (m = 2). They proved the local existence, global existence and finite time blow-up of solutions as well as the estimation on the potential well ... See full document

... 2kT-periodic solutions for a kind of prescribed mean curvature Duffing-type equation is studied, and then a homoclinic solution is obtained as a limit of a certain subsequence of the above ... See full document

... Therefore, it has been seen how (1) emerges and that physical classes of solutions to (2) can be investigated. Most importantly, a link between the wavefunctions im- plied by the model and the calculation of a ... See full document

... the semilinear condition at infinity and the time map satisfies an os- cillation condition, and prove that the given equation possesses infinitely many positive π-periodic solutions by using the ... See full document

... symmetric solutions of the nonlinear Klein-Gordon equation for the same nonlinear term we study in this paper; one of the most important features of their numerical method was that the ... See full document

... inhomogeneous norm, and so it lacks the homogeneity property: kf |k|f. However, for nonlinear problems such as 1.3, the homogeneity property may not be an essential factor— we try to explain that the new space ... See full document

... Hindawi Publishing Corporation Advances in Difference Equations Volume 2009, Article ID 463169, 11 pages doi 10 1155/2009/463169 Research Article On Boundedness of Solutions of the Difference Equation[.] ... See full document