Multisummability of Formal Solutions of Singular Perturbation Problems

Asymptotic Solutions of Singular Perturbation Problems for Linear Differential Equations of Elliptic Type

On some anisotropic singular perturbation problems

We investigate the asymptotic behavior of some anisotropic diffusion problems and give some estimates on the rate of convergence of the solution toward its limit. We also relate this type of elliptic problems to problems set in cylinder becoming unbounded in some directions and show how some information on one type leads to information for the other type and conversely. 1. A model problem The g...

Existence and instability of spike layer solutions to singular perturbation problems

An abstract framework is given to establish the existence and compute the Morse index of spike layer solutions of singularly perturbed semilinear elliptic equations. A nonlinear Lyapunov–Schmidt scheme is used to reduce the problem to one on a normally hyperbolic manifold, and the related linearized problem is also analyzed using this reduction. As an application, we show the existence of a mul...

Solutions of Nonlinear Integral Equations and Their Application to Singular Perturbation Problems Thesis By

Sufficient conditions for the existence and uniqueness, and estimates, of a continuous vector solution y = y(t) to the integral equation y(t) = u(t) + EL(t) Ef t M(s) f(s,y(s)) ds + K(t,s) f(s,y(s)) ds, t 0 are derived. A successive approximation technique involving a double sequence is used in the proof . This integral equation result is applied to the second order singular perturbation proble...

Multiplicity of solutions for critical singular problems

[1] R. B. Assunção, P. C. Carrião, O. H. Miyagaki, Multiplicity of solutions for critical singular problems, Applied Mathematics Letters 19 (2006) 741–746. [2] R. B. Assunção, P. C. Carrião, O. H. Miyagaki, Critical singular problems via concentration-compactness lemma, J. Math. Anal. Appl. 326 (2007), 137–154. [3] J. Chen, S. Li, On multiple solutions of a singular quasilinear equation on unbo...