On the number of closed solutions to an equation \(\dot x=f(t,x)\), where \(f_{x^ n}(t,x)\geq 0\) (n=1,2,or 3)

DOI10.1016/0022-247X(91)90225-OzbMath0732.34039OpenAlexW2058143884MaRDI QIDQ809250

Kurt Munk Andersen, Allan Sandqvist

Publication date: 1991

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-247x(91)90225-o

zbMATH Keywords

stability propertiescharacteristic exponentclosed solutionsT- periodic solutions

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25)

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The number of bifurcation points of a periodic one-parameter ODE with at most two periodic solutions, The set of periodic scalar differential equations with cubic nonlinearities, On the determination of the number of periodic (or closed) solutions of a scalar differential equation with convexity, On the interaction of species capable of explosive growth, On the number of limit cycles of a generalized Abel equation, A criterion for the existence of the unique periodic solution of one-dimensional periodic differential equation, Existence of closed solutions of an equation \(\dot x=f(t,x)\), where \(f_x'(t,x)\) is weakly convex or concave in \(x\), Existence of periodic solutions for fully nonlinear first-order differential equations

Cites Work

• On the number of solutions of the equation \(\sum^n_{j=0}a_j(t)x^j,0\leq t\leq 1\), for which \(x(0)=x(1)\)
• A necessary and sufficient condition for the existence of a unique nontrivial periodic solution to a class of equations of Lienards type
• Periodic Equilibria under Periodic Harvesting
• Periodic solutions of polynomial first order differential equations
• Some Results Concerning Periodic Solutions of Plane Autonomous Differential Systems