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Heteroclinic solutions in singularly perturbed discontinuous differential equations: a non-generic case

open access: yesElectronic Journal of Qualitative Theory of Differential Equations
We derive Melnikov type conditions for the persistence of heteroclinic solutions in perturbed slowly varying discontinuous differential equations. Opposite to [J. Differential Equations 400(2024), 314–375] we assume that the unperturbed (frozen) equation
Flaviano Battelli   +2 more
doaj   +1 more source

Singularly perturbed ordinary differential equations

open access: yesJournal of Mathematical Analysis and Applications, 1992
Consider abstract nonlinear equations of the form (*) \(Lu+\varepsilon F(u,v)=0\), \(S(v)+\varepsilon V(u,v)=0\) where \(L\) is linear, \(\varepsilon\) is a small parameter. By using the coincidence degree the author derives conditions on the operators such that (*) has a solution.
openaire   +1 more source

Singularly perturbed discrete differential equations

open access: yes
Discrete differential equations appear most prominently in planar map and lattice path enumeration. In this work we consider discrete differential equations with an additional parameter $x$, where the order of the equation is $1$ for $x=0$ but $k> 1$ for $x\ne 0$. We call such equations singularly perturbed.
Drmota, Michael, Hainzl, Eva-Maria
openaire   +2 more sources

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