Open Access Research

Existence and multiplicity of solutions for some second-order systems on time scales with impulsive effects

Jianwen Zhou1, Yanning Wang2 and Yongkun Li1*

Author Affiliations

1 Department of Mathematics, Yunnan University, Kunming, Yunnan, 650091, People’s Republic of China

2 Oxbridge College, Kunming University of Science and Technology, Kunming, Yunnan, 650106, People’s Republic of China

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Boundary Value Problems 2012, 2012:148  doi:10.1186/1687-2770-2012-148

Published: 21 December 2012

Abstract

In this paper, we present a recent approach via variational methods and critical point theory to obtain the existence of solutions for the nonautonomous second-order system on time scales with impulsive effects

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where <a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/148/mathml/M2','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/148/mathml/M2">View MathML</a>, <a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/148/mathml/M3','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/148/mathml/M3">View MathML</a> (<a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/148/mathml/M4','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/148/mathml/M4">View MathML</a>), <a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/148/mathml/M5','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/148/mathml/M5">View MathML</a>, <a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/148/mathml/M6','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/148/mathml/M6">View MathML</a> is a symmetric <a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/148/mathml/M7','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/148/mathml/M7">View MathML</a> matrix-valued function defined on <a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/148/mathml/M8','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/148/mathml/M8">View MathML</a> with <a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/148/mathml/M9','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/148/mathml/M9">View MathML</a> for all <a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/148/mathml/M10','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/148/mathml/M10">View MathML</a>, <a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/148/mathml/M11','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/148/mathml/M11">View MathML</a> (<a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/148/mathml/M12','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/148/mathml/M12">View MathML</a>, <a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/148/mathml/M13','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/148/mathml/M13">View MathML</a>) are continuous and <a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/148/mathml/M14','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/148/mathml/M14">View MathML</a>. Finally, two examples are presented to illustrate the feasibility and effectiveness of our results.

MSC: 34B37, 34N05.

Keywords:
nonautonomous second-order systems; time scales; impulse; variational approach