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Ordinary Differential Equations and Applied Dynamics Commons™
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- Boundary value problems (2)
- Fixed point theorem (2)
- Green's function (2)
- Journal articles (2)
- Local fractional derivative (2)
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- <p>Differential equations.</p> <p>Difference equations.</p> <p>Differentiable dynamical systems.</p> (1)
- <p>Fixed point theory.</p> <p>Boundary value problems.</p> <p>Green's function.</p> (1)
- Blow-up solutions (1)
- Combustion (1)
- Conference articles (1)
- Continuous solution (1)
- Eigenvalues (1)
- Fractal Griffith’s crack (1)
- Fractal calculus (1)
- J-integral (1)
- Local fractional definite integral (1)
- Local fractional integral (1)
- M.S. thesis (1)
- Mean value theorems (1)
- Positive solutions (1)
- Properties (1)
- Reaction-diffusion systems (1)
- Resonance (1)
- Rolle’s theorem (1)
- Semilinear wave equation (1)
- Theorems (1)
- Twin positive solutions (1)
- Uniqueness of local fractional derivative (1)
- Virtual work principle (1)
- Volterra equations (1)
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Articles 1 - 8 of 8
Full-Text Articles in Ordinary Differential Equations and Applied Dynamics
A Semilinear Wave Equation With Smooth Data And No Resonance Having No Continuous Solution, Jose F. Caicedo, Alfonso Castro
A Semilinear Wave Equation With Smooth Data And No Resonance Having No Continuous Solution, Jose F. Caicedo, Alfonso Castro
All HMC Faculty Publications and Research
We prove that a boundary value problem for a semilinear wave equation with smooth nonlinearity, smooth forcing, and no resonance cannot have continuous solutions. Our proof shows that this is due to the non-monotonicity of the nonlinearity.
An Adaptive Method For Calculating Blow-Up Solutions, Charles F. Touron
An Adaptive Method For Calculating Blow-Up Solutions, Charles F. Touron
Mathematics & Statistics Theses & Dissertations
Reactive-diffusive systems modeling physical phenomena in certain situations develop a singularity at a finite value of the independent variable referred to as "blow-up." The attempt to find the blow-up time analytically is most often impossible, thus requiring a numerical determination of the value. The numerical methods often use a priori knowledge of the blow-up solution such as monotonicity or self-similarity. For equations where such a priori knowledge is unavailable, ad hoc methods were constructed. The object of this research is to develop a simple and consistent approach to find numerically the blow-up solution without having a priori knowledge or resorting …
Research On Fractal Mathematics And Some Application In Mechanics, Yang Xiaojun
Research On Fractal Mathematics And Some Application In Mechanics, Yang Xiaojun
Xiao-Jun Yang
Since Mandelbrot proposed the concept of fractal in 1970s’, fractal has been applied in various areas such as science, economics, cultures and arts because of the universality of fractal phenomena. It provides a new analytical tool to reveal the complexity of the real world. Nowadays the calculus in a fractal space becomes a hot topic in the world. Based on the established definitions of fractal derivative and fractal integral, the fundamental theorems of fractal derivatives and fractal integrals are investigated in detail. The fractal double integral and fractal triple integral are discussed and the variational principle in fractal space has …
The Fundamentals Of Local Fractional Derivative Of The One-Variable Non-Differentiable Functions, Yang Xiaojun
The Fundamentals Of Local Fractional Derivative Of The One-Variable Non-Differentiable Functions, Yang Xiaojun
Xiao-Jun Yang
Based on the theory of Jumarie’s fractional calculus, local fractional derivative is modified in detail and its fundamentals of local fractional derivative are proposed in this paper. The uniqueness of local fractional derivative is obtained and the Rolle’s theorem, the mean value theorem, the Cauchy’s generalized mean value theorem and the L’Hospital’s rules are proved.
Local Fractional Newton’S Method Derived From Modified Local Fractional Calculus, Yang Xiao-Jun
Local Fractional Newton’S Method Derived From Modified Local Fractional Calculus, Yang Xiao-Jun
Xiao-Jun Yang
A local fractional Newton’s method, which is derived from the modified local fractional calculus , is proposed in the present paper. Its iterative function is obtained and the convergence of the iterative function is discussed. The comparison between the classical Newton iteration and the local fractional Newton iteration has been carried out. It is shown that the iterative value of the local fractional Newton method better approximates the real-value than that of the classical one.
Finding Positive Solutions Of Boundary Value Dynamic Equations On Time Scale, Olusegun Michael Otunuga
Finding Positive Solutions Of Boundary Value Dynamic Equations On Time Scale, Olusegun Michael Otunuga
Theses, Dissertations and Capstones
This thesis is on the study of dynamic equations on time scale. Most often, the derivatives and anti-derivatives of functions are taken on the domain of real numbers, which cannot be used to solve some models like insect populations that are continuous while in season and then follow a difference scheme with variable step-size. They die out in winter, while the eggs are incubating or dormant; and then they hatch in a new season, giving rise to a non overlapping population. The general idea of my thesis is to find the conditions for having a positive solution of any boundary …
Twin Solutions Of Even Order Boundary Value Problems For Ordinary Differential Equations And Finite Difference Equations, Xun Sun
Theses, Dissertations and Capstones
The Avery-Henderson fixed-point theorem is first applied to obtain the existence of at least two positive solutions for the boundary value problem
(-1)ny(2n) = f(y); n = 1; 2; 3 ... and t 2 [0; 1];
with boundary conditions
y(2k)(0) = 0
y(2k+1)(1) = 0 for k = 0; 1; 2 ... n - 1:
This theorem is subsequently used to obtain the existence of at least two positive solutions for the dynamic boundary value problem
(-1)n (2n)u(k)g(u(k)); n = 1; 2; 3 .... and k (0; ... N);
with boundary conditions
(2k)u(0) …
Problems Of Local Fractional Definite Integral Of The One-Variable Non-Differentiable Function, Yang Xiao-Jun
Problems Of Local Fractional Definite Integral Of The One-Variable Non-Differentiable Function, Yang Xiao-Jun
Xiao-Jun Yang
It is proposed that local fractional calculas introduced by Kolwankar and Gangal is extended by the concept of Jumarie’s fractional calculus and local fractional definite integral is redefined. The properties and the theorems of local fractional calculus are discussed in this paper.