Higher-order nonlinear terms
CONTRIBUTION OF HIGHER ORDER TERMS TO THE NONLINEAR SHALLOW WATER WAVES
... weakly nonlinear waves in shallow water and obtained the gov- erning evolution equations of various order terms in the perturbation ...correction terms so as to remove some possible ...th ...
9
Eigenvalues of higher order Sturm-Liouville boundary value problems with derivatives in nonlinear terms
... derivative-dependent nonlinear term, which makes the investigation much more challenging. In this paper we shall develop a new technique to characterize the eigenvalues λ so that the boundary value problem has a ...
22
Positive solutions of higher order Sturm–Liouville boundary value problems with fully nonlinear terms
... αu (n–2) (0) – βu (n–1) (0) = 0, γ u (n–2) (1) + δu (n–1) (1) = 0, (1.5) where 1 ≤ q ≤ n – 2. They converted BVP (1.5) to an equivalent (m – q)th-order Sturm– Liouville boundary value problem of ...
20
Positive solutions of higher-order Sturm-Liouville boundary value problems with derivative-dependent nonlinear terms
... y (m) (t) + F(t, y(t), y (t), . . . , y (q) (t)) = 0, t ∈ [0, 1], y (k) (0) = 0, 0 ≤ k ≤ m – 3, ζ y (m–2) (0) – θ y (m–1) (0) = 0, ρ y (m–2) (1) + δ y (m–1) (1) = 0, where m ≥ 3 and 1 ≤ q ≤ m – 2. We note that the ...
25
Index Terms --nonlinear systems, stability analysis, Lyapunov functions, higher order derivatives, homogeneous systems.
... for nonlinear dynamic systems needs a positive definite function whose time derivative is at least negative semi-definite in the direction of the system’s ...of higher order derivatives of the ...
6
Nonlinear Control Design Techniques Via Higher Order Lyapunov Functions.
... required nonlinear state feedback control problems based on polynomial sys- tems with and without input saturations, Chapter 3 and Chapter 4 demonstrated the advantage of using power transformation to derive ...
127
Higher Order WHEP Solutions of Quadratic Nonlinear Stochastic Oscillatory Equation
... tic PDEs repeatedly for many realizations. Instead, the deterministic system is solved only once. The application of the WHE [4-10] aims at finding a truncated series solution to the solution process of a sto- chastic ...
13
Higher order approximate periodic solutions for nonlinear oscillators with the Hamiltonian approach
... of nonlinear equations in mechanics and physics is of interest to many ...solving nonlinear equations, such as the energy balance method [1–8], the frequency amplitude formulation [9–12], the variational ...
10
Existence of Random Attractor Family for a Class of Nonlinear Higher Order Kirchhoff Equations
... noise terms. In recent years, stochastic attractors for stochastic nonlinear equations with white noise have been favored by many scholars, and many scholars have done a lot of research on these problems ...
12
A higher order method for nonlinear singular two point boundary value problems
... less order than the error term | y − y ¯ 1 | , then more accuracy may be achieved by taking more terms in the expan- sion of g about y 1 ...of order 1, wU 0 + m+1 , where m is the number of ...
13
Fundamental Solitons For The Higher-order Nonlinear Schrödinger Equation With A Pt -symmetric Potential
... fourth order dispersion term γu xxxx on the soliton properties and their ...cubic nonlinear Schrödinger equation without a PT -symmetric potential, as it is stated [4], this equation represent the ...
67
Long-Time Behavior of Solutions for a Class of Nonlinear Higher Order Kirchhoff Equation
... On the basis of the lower-order Kirchhoff-type equation studied by previous scholars, this paper studies the global attractor family and its finite dimension estimation for the higher-order ...
9
NONLINEAR BENDING ANALYSIS OF FUNCTIONALLY GRADED PLATES USING HIGHER ORDER THEORY
... first order shear deformation theory are the simplest equivalent single layer theories and they adequately describe the kinematic behavior of most functionally graded ...materials. Higher-order ...
13
Higher-Order Nonlinear Schrödinger Equation Family in Optical Fiber and Solitary Wave Solutions
... highly nonlinear partial differential equation, which initially governs the dynamics of the propagation in such a wave ...various terms of the established nonlinear partial differential equation, ...
11
Existence and Asymptotic Behavior of Global Solutions for a Class of Nonlinear Higher Order Wave Equation
... for higher-order wave equations,” Acta Mathematica ...a nonlinear wave equation with nonlinear damping and source terms,” Journal of Mathematical Analysis and Applications, ...
14
ATTRACTIVITY OF A HIGHER ORDER NONLINEAR DIFFERENCE EQUATION
... A Monthly Double-Blind Peer Reviewed Refereed Open Access International e-Journal - Included in the International Serial Directories International Journal in IT and Engineering http://www.ijmr.net.in email id- ...
12
On the oscillation of higher order nonlinear neutral difference equations
... Abstract In this paper, we shall investigate some oscillation criteria for the solutions of mth-order nonlinear neutral difference equation where m ≥ 1. The results presented here complement some of the ...
10
A Transfinite Knuth-Bendix Order for Lambda-Free Higher-Order Terms
... λ-free higher-order term rewriting systems or, equiva- lently, applicative term rewriting systems ...reduction order: a well-founded partial order that is compatible with contexts and stable ...
20
Existence of positive solutions of higher order nonlinear neutral equations
... of higher-order nonlinear neutral differential ...In order to obtain new sufficient conditions for the existence of a positive solution, we use Schauder’s fixed point ...
10
Solvability of a Higher Order Nonlinear Neutral Delay Difference Equation
... Copyright q 2010 M. Liu and Z. Guo. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the ...
14