Homoclinic solutions to an integral equation: Existence and stability. (English) Zbl 0934.45005
The authors study (stationary) evolution equation in the form of the following nonlinear convolution type integral equation
\[
(J\ast u)(x)- u(x)-f[u(x)]=0,\tag{1}
\]
with the condition \(u(\pm \infty)=0.\) It is assumed, that \(J(z)\geq 0\), \(\int J(z) dz =1\) and \(f\) is bistable. They construct homoclinic (even) solutions to the equation (1).
Reviewer: N.K.Karapetyants (Rostov-na-Donu)
Keywords:
homoclinic solutions; evolution equations; stability; nonlinear convolution type integral equationReferences:
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