Uniqueness of solutions for the extendedFisher -
نویسنده
چکیده
We consider stationary solutions of the Extended Fisher-Kolmogorov (EFK) equation , a fourth-order model equation for bi-stable systems. We show that as long as the stable equilibrium points are real saddles, the paths in the (u; u 0)-plane of two bounded solutions do not cross. As a consequence we derive that the bounded solutions of the EFK equation correspond exactly to those of the classical Fisher Kolmogorov equation. On examine les solutions stationnaires de l' equation etendue de Fisher-Kolmogorov (EFK), une equation mod ele du quatri eme ordre pour des syst emes bi-stables. Nous montrons que tant que les points d' equilibre stables sont des`real saddles', les tra-jectoires dans le (u; u 0)-plan de deux solutions born ees ne se croisent pas. Comme cons equence nous d erivons que les solutions born ees de l' equation EFK correspondent exactement a celles de l' equation classique de Fisher-Kolmogorov.
منابع مشابه
Existence and uniqueness of weak solutions for a class of nonlinear divergence type diffusion equations
In this paper, we study the Neumann boundary value problem of a class of nonlinear divergence type diffusion equations. By a priori estimates, difference and variation techniques, we establish the existence and uniqueness of weak solutions of this problem.
متن کاملExistence and uniqueness of solutions for p-laplacian fractional order boundary value problems
In this paper, we study sufficient conditions for existence and uniqueness of solutions of three point boundary vale problem for p-Laplacian fractional order differential equations. We use Schauder's fixed point theorem for existence of solutions and concavity of the operator for uniqueness of solution. We include some examples to show the applicability of our results.
متن کاملA novel existence and uniqueness theorem for solutions to FDEs driven by Lius process with weak Lipschitz coefficients
This paper we investigate the existence and uniqueness of solutions to fuzzydierential equations driven by Liu's process. For this, it is necessary to provideand prove a new existence and uniqueness theorem for fuzzy dierential equationsunder weak Lipschitz condition. Then the results allows us to considerand analyze solutions to a wide range of nonlinear fuzzy dierential equationsdriven by Liu...
متن کاملThe Uniqueness Theorem for the Solutions of Dual Equations of Sturm-Liouville Problems with Singular Points and Turning Points
In this paper, linear second-order differential equations of Sturm-Liouville type having a finite number of singularities and turning points in a finite interval are investigated. First, we obtain the dual equations associated with the Sturm-Liouville equation. Then, we prove the uniqueness theorem for the solutions of dual initial value problems.
متن کاملExistence and Uniqueness Results for a Nonstandard Variational-Hemivariational Inequalities with Application
This paper aims at establishing the existence and uniqueness of solutions for a nonstandard variational-hemivariational inequality. The solutions of this inequality are discussed in a subset $K$ of a reflexive Banach space $X$. Firstly, we prove the existence of solutions in the case of bounded closed and convex subsets. Secondly, we also prove the case when $K$ is compact convex subsets. Fina...
متن کاملExistence and uniqueness of solutions for a periodic boundary value problem
In this paper, using the fixed point theory in cone metric spaces, we prove the existence of a unique solution to a first-order ordinary differential equation with periodic boundary conditions in Banach spaces admitting the existence of a lower solution.
متن کامل