Heteroclinic solutions of singular Φ-Laplacian boundary value problems on infinite time scales

Prasad, K. Venkatesh; Murali, P.

doi:10.14232/ejqtde.2012.1.86

Cited by 2 publications

(1 citation statement)

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“…We highlight that our paper is devoted to equations on time scales that involve a ϕ-laplacian of relativistic type, for which the literature is scarce. For example, in [16], the existence of heteroclinic solutions for a family of equations on time scales that includes the unforced relativistic pendulum is proved. However, to our knowledge there are no papers concerned with periodic solutions and, more precisely, the solvability set for equations with a singular ϕ-laplacian on time scales.…”

Section: Introductionmentioning

confidence: 99%

On the Solvability of the Periodically Forced Relativistic Pendulum Equation on Time Scales

Amster¹,

Kuna²,

Santos³

2020

Preprint

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We study some properties of the range of the relativistic pendulum operator P, that is, the set of possible continuous T -periodic forcing terms p for which the equation Px = p admits a T -periodic solution over a Tperiodic time scale T. Writing p(t) = p0(t) + p, we prove the existence of a nonempty compact interval I(p0), depending continuously on p0, such that the problem has a solution if and only if p ∈ I(p0) and at least two different solutions when p is an interior point. Furthermore, we give sufficient conditions for nondegeneracy; specifically, we prove that if T is small then I(p0) is a neighbourhood of 0 for arbitrary p0. The results in the present paper improve the smallness condition obtained in previous works for the continuous case T = R.

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Section: Introductionmentioning

confidence: 99%