We analyze the existence of T −periodic solutions to the second-order indefinite singular equation u ′′ = β h(t) cos 2 u which depends on a positive parameter β > 0. Here, h is a sign-changing function with h = 0 and where the nonlinear term of the equation has two singularities. For the first time, the degenerate case is studied, displaying an unexpected feature which contrasts with the results known in the literature for indefinite singular equations.

We analyze the existence and uniqueness of monotone traveling wavefront for a generalized nonlinear Klein–Gordon model ∂2ϕ∂t2−p+∂ϕ∂x2∂2ϕ∂x2+V′(ϕ)=0, using classical arguments of ordinary differential equations, with V(x) a potentials family containing the ϕ‐four potential Vfalse(xfalse)=M0false(1−x2false)2 and the sine‐Gordon‐type potential Vfalse(xfalse)=false(1false/2false)false(1+cosfalse(πxfalse)false). Also for these specific potentials, we give estimations of their monotone kink and anti‐kink solutions.

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Communicated by M. GrovesIn this work, we study the approximation of traveling wave solutions propagated at minumum speeds c 0 .h/ of the delayed Nicholson's blowflies equation:. /In order to do that, we construct a subsolution and a super solution to . /. Also, through that construction, an alternative proof of the existence of traveling waves moving at minimum speed is given. Our basic hypothesis is that p=ı 2 .1, e and then, the monostability of the reaction term.