An argument of this nature may be adapted to more general uniformly elliptic second order partial differential operators via unique continuation principles; see, for instance, [2, 3, 20, 23, 25, 26, 38].
In [22, 24 45], the authors investigated the existence and exponential stability of anti-periodic solutions for some neural networks by applying the differential inequality techniques, the continuation theorem of coincidence degree theory, the contraction mapping principle, and the Lyapunov functional method, respectively.
Numerical continuation calculations for ordinary differential equations (ODEs) are, by now, an established tool for bifurcation analysis in dynamical systems theory as well as across almost all natural and engineering sciences.
Refinements of the design are carried out using gradient based methods such as differential correction and pseudo arc length continuation method under the of circular restricted three body model.
Our proofs rely on Schauder's fixed point theorem and some extensions of the continuation theorems for ordinary differential equations (ODEs) to the fractional order case.
In Refs. [6, 9], the authors studied the existence of solutions for functional boundary value problems with a linear differential operator by using Mawhin's continuation theorem.
In past decades, many authors investigated the existence of periodic solutions for p-Laplacian differential equations by using Mawhin's continuation theorem, for more details, see e.g. [10 15] for work on this subject.
The unique continuation theorems for elliptic differential-operator equations with variable coefficients in vector-valued L p -space are investigated.
Although several excellent standard software packages are available for ODEs, there are - for good reasons - no standard numerical continuation toolboxes available for partial differential equations (PDEs), which cover a broad range of different classes of PDEs automatically.
