Abstract
In this paper, we consider a kind of p-Laplacian neutral Rayleigh equation with singularity of attractive type, \t\t\t(ϕp(u(t)−cu(t−δ))′)′+f(t,u′(t))+g(t,u(t))=e(t).\\documentclass[12pt]{minimal}\t\t\t\t\\usepackage{amsmath}\t\t\t\t\\usepackage{wasysym}\t\t\t\t\\usepackage{amsfonts}\t\t\t\t\\usepackage{amssymb}\t\t\t\t\\usepackage{amsbsy}\t\t\t\t\\usepackage{mathrsfs}\t\t\t\t\\usepackage{upgreek}\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\t\t\t\t\\begin{document}$$\\bigl(\\phi_{p} \\bigl(u(t)-cu(t-\\delta) \\bigr)' \\bigr)'+f \\bigl(t,u'(t) \\bigr)+g \\bigl(t, u(t) \\bigr)=e(t). $$\\end{document} By applications of an extension of Mawhin’s continuation theorem, sufficient conditions for the existence of periodic solution are established.
Highlights
As is well known, the Rayleigh equation can be derived from many fields, such as physics, mechanics and engineering technique fields, and an important question is whether this equation can support periodic solutions
In this paper, we consider a kind of p-Laplacian neutral Rayleigh equation with singularity of attractive type, (φp(u(t) – cu(t – δ)) ) + f (t, u (t)) + g(t, u(t)) = e(t)
5 Conclusions In this article we introduce the existence of a periodic solution for a p-Laplacian neutral Rayleigh equation with singularity of attractive type
Summary
The Rayleigh equation can be derived from many fields, such as physics, mechanics and engineering technique fields, and an important question is whether this equation can support periodic solutions. Abstract In this paper, we consider a kind of p-Laplacian neutral Rayleigh equation with singularity of attractive type, (φp(u(t) – cu(t – δ)) ) + f (t, u (t)) + g(t, u(t)) = e(t). By applications of an extension of Mawhin’s continuation theorem, sufficient conditions for the existence of periodic solution are established.
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