Landesman-Lazer type condition and nonlinearities with linear growth
Laplace Adomian decomposition method for solving a fish farm model
In this work, a combined form of the Laplace transform method and the Adomian decomposition method is implemented to give an approximate solution of nonlinear systems of differential equations such as fish farm model with three components nutrient, fish and mussel. The technique is described and illustrated with a numerical example.
Least squares completions for nonlinear differential algebraic equations.
Linearization Of Nonlinear Differential Equations: Third Order Nonlinear Ordinary Differential Equations Equivalent To Linear Second Order Equations
Linearly Implicit Extrapolation Methods for Differential-Algebraic Systems.
Local method of nonlinear analysis
Lösung von Differentialgleichungen mit Splinefunktionen. Eine Störungstheorie. Tei 1: Divergenzaussagen.
Lotka-Volterra type predator-prey models: Comparison of hidden and explicit resources with a transmissible disease in the predator species
The paper deals with two mathematical models of predator-prey type where a transmissible disease spreads among the predator species only. The proposed models are analyzed and compared in order to assess the influence of hidden and explicit alternative resource for predator. The analysis shows boundedness as well as local stability and transcritical bifurcations for equilibria of systems. Numerical simulations support our theoretical analysis.
Lyapunov type integral inequalities for certain differential equations.
Mathematical description of the phase transition curve near the critical point
In this paper, by applying a simple mathematical model imitating the equation of state, behaviour of the phase transition curve near the critical point is investigated. The problem of finding the unique vapour-liquid equilibrium curve passing through the critical point is reduced to solving a nonlinear system of differential equations.
Method of successive approximations for a certain nonlinear third order boundary value problem
Model reduction methods for chaotic systems
Modelling Tuberculosis and Hepatitis B Co-infections
Tuberculosis (TB) is the leading cause of death among individuals infected with the hepatitis B virus (HBV). The study of the joint dynamics of HBV and TB present formidable mathematical challenges due to the fact that the models of transmission are quite distinct. We formulate and analyze a deterministic mathematical model which incorporates of the co-dynamics of hepatitis B and tuberculosis. Two sub-models, namely: HBV-only and TB-only sub-models...
Modified Adomian decomposition method for singular initial value problems in the second-order ordinary differential equations.
Monotonicity theorems for second order non-linear differential equations
Morales-Ramis Theorems via Malgrange pseudogroup
In this article we give an obstruction to integrability by quadratures of an ordinary differential equation on the differential Galois group of variational equations of any order along a particular solution. In Hamiltonian situation the condition on the Galois group gives Morales-Ramis-Simó theorem. The main tools used are Malgrange pseudogroup of a vector field and Artin approximation theorem.
Motion of spiral-shaped polygonal curves by nonlinear crystalline motion with a rotating tip motion
We consider a motion of spiral-shaped piecewise linear curves governed by a crystalline curvature flow with a driving force and a tip motion which is a simple model of a step motion of a crystal surface. We extend our previous result on global existence of a spiral-shaped solution to a linear crystalline motion for a power type nonlinear crystalline motion with a given rotating tip motion. We show that self-intersection of the solution curves never occurs and also show that facet extinction never...
Multiple solutions for a nonlinear second order differential equation
Multiplicity of positive solutions for a nonlinear differential equation with nonlinear boundary conditions
We study the existence and multiplicity of positive solutions of the nonlinear equation u''(x) + λh(x)f(u(x)) = 0 subject to nonlinear boundary conditions. The method of upper and lower solutions and degree theory arguments are used.
Multi-Step Methods are Essentially One-Step Methods.