5,713 research outputs found
Positive periodic solutions of singular systems
The existence and multiplicity of positive periodic solutions for second
order non-autonomous singular dynamical systems are established with
superlinearity or sublinearity assumptions at infinity for an appropriately
chosen parameter. Our results provide a unified treatment for the problem and
significantly improve several results in the literature. The proof of our
results is based on the Krasnoselskii fixed point theorem in a cone.Comment: Journal of Differential Equations, 201
Traveling Wave Solutions of a Reaction-Diffusion Equation with State-Dependent Delay
This paper is concerned with the traveling wave solutions of a
reaction-diffusion equation with state-dependent delay. When the birth function
is monotone, the existence and nonexistence of monotone traveling wave
solutions are established. When the birth function is not monotone, the minimal
wave speed of nontrivial traveling wave solutions is obtained. The results are
proved by the construction of upper and lower solutions and application of the
fixed point theorem
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