Abstract:In the present work, we deal with nonlinear fractional differential equations with "maxima" and deviating arguments. The nonlinear part of the problem under consideration depends on the maximum values of the unknown function taken in time-dependent intervals. Proceeding by an iterative approach, we obtain the existence and uniqueness of the solution, in a context that does not fit within the framework of fixed point theory methods for the self-mappings, frequently used in the study of such problems. An example illustrating our main result is also given.
In this paper, we investigate the existence and uniqueness of solutions for functional impulsive fractional differential equations and integral boundary conditions. Our results are based on some fixed point theorems. Finally, we provide an example to illustrate the validity of our main results.
We consider a nonlinear two-dimensional Kuramoto-Sivashinsky equation, with nonlocal source, and by a reduction method we determine a class of spatially periodic steady state solutions. Our analysis leads toward some computation, which can be easily automatized. By use of the symmetries of the problem we study the structure of the reduced equation, and we obtain an algebraic system of lower order, determining all the small solutions to the stationary problem.
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