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A note on an approximative scheme of finding almost homoclinic solutions for Newtonian systems

100%

Krawczyk R.

Banach Center Publications

2014

tom 101

nr 1

107-113

In this work we will be concerned with the existence of almost homoclinic solutions for a Newtonian system $q̈ + ∇_{q}V(t,q) = f(t)$, where t ∈ ℝ, q ∈ ℝⁿ. It is assumed that a potential V: ℝ × ℝⁿ → ℝ is C¹-smooth and its gradient map $∇_{q}V: ℝ × ℝⁿ → ℝⁿ$ is bounded with respect to t. Moreover, a forcing term f: ℝ → ℝⁿ is continuous, bounded and square integrable. We will show that the approximative scheme due to J. Janczewska (see [J2]) for a time periodic potential extends to our case.

Homoclinic orbits for an almost periodically forced singular Newtonian system in ℝ³

100%

Krawczyk R.

Annales Polonici Mathematici

2015

tom 114

nr 1

29-43

This work uses a variational approach to establish the existence of at least two homoclinic solutions for a family of singular Newtonian systems in ℝ³ which are subjected to almost periodic forcing in time variable.

Ograniczanie wyników

1 Annales Polonici Mathematici

1 Banach Center Publications

2 Krawczyk R.

1 2015

1 2014

Wyniki wyszukiwania

A note on an approximative scheme of finding almost homoclinic solutions for Newtonian systems

Homoclinic orbits for an almost periodically forced singular Newtonian system in ℝ³