Stability of traveling wavefronts for the discrete Nagumo equation
SIAM Journal on Mathematical Analysis
Circularly symmetric deformation of shallow elastic membrane caps
Quarterly of Applied Mathematics
Nonpositone discrete boundary value problems
Nonlinear Analysis: Theory, Methods & Applications
On the existence of positive solutions of p-Laplacian difference equations
Journal of Computational and Applied Mathematics
| Hi-index | 0.98 |
For each n@?N, n=2, we prove the existence of a solution (u"0,...,u"n)@?R^n^+^1 of the singular discrete problem 1h^2@D^2u"k"-"1+f(t"k,u"k)=0,k=1,...,n-1,@Du"0=0,u"n=0, where u"k0 for k=0,...,n-1. Here T@?(0,~), h=Tn, t"k=hk, f(t,x):[0,T]x(0,~)-R is continuous and has a singularity at x=0. We prove that for n-~ the sequence of solutions of the above discrete problems converges to a solution y of the corresponding continuous boundary value problem y^''(t)+f(t,y(t))=0,y^'(0)=0,y(T)=0.