Differentiation of solutions of dynamic equations on time scales with respect to parameters

V tomto clanku dokazujeme diferencovatelnost řeseni nelinearnich dynamických rovnic na casových skalach vzhledem k parametrům. Toto doplňuje předchozi praci prvniho a třetiho autora ohledně existence a spojite zavislosti řeseni na parametrech. Dale se specialně věnujeme dynamickým rovnicim na casových skalach, ktere jsou linearni vzhledem k nezname funkci a parametru. Pro tento připad odvozujeme vylepsený výsledek, který řika, že řeseni je cela funkce vzhledem k parametru.

[1]  P. Hartman.  Ordinary Differential Equations , 1965 .

[2]  V. Lakshmikantham,et al.  Dynamic systems on measure chains , 1996 .

[3]  Chao Zhang,et al.  Eigenvalues of second-order symmetric equations on time scales with periodic and antiperiodic boundary conditions , 2008, Appl. Math. Comput..

[4]  V. Zeidan,et al.  Time scale symplectic systems without normality , 2006 .

[5]  Markus Wahrheit.  Eigenvalue Problems and Oscillation of Linear Hamiltonian Systems , 2007 .

[6]  Martin Bohner.  CALCULUS OF VARIATIONS ON TIME SCALES , 2004 .

[7]  A. Peterson,et al.  Inequalities on Time Scales: A Survey , 2001 .

[8]  Dennis S. Bernstein,et al.  Matrix Mathematics: Theory, Facts, and Formulas with Application to Linear Systems Theory , 2005 .

[9]  Martin Bohner,et al.  AN EIGENVALUE PROBLEM FOR LINEAR HAMILTONIAN DYNAMIC SYSTEMS , 2005 .

[10]  Werner Kratz,et al.  Quadratic Functionals in Variational Analysis and Control Theory , 1995 .

[11]  A. Peterson,et al.  Dynamic Equations on Time Scales , 2001 .

[12]  Asymptotic expansions and analytic dynamic equations , 2006 .

[13]  Martin Bohner,et al.  Hamiltonian Systems on Time Scales , 2000 .

[14]  Martin Bohner,et al.  Sturmian and spectral theory for discrete symplectic systems , 2009 .

[15]  M. Connor.  Calculus of Variations and Optimal Control Theory , 1967 .

[16]  Vera Zeidan,et al.  The conjugate point condition for smooth control sets , 1988 .

[17]  N. G. Parke,et al.  Ordinary Differential Equations. , 1958 .

[18]  Vera Zeidan,et al.  Time scale embedding theorem and coercivity of quadratic functionals , 2008 .

[19]  A. Peterson,et al.  Dynamic Equations on Time Scales: An Introduction with Applications , 2001 .

[20]  Vera Zeidan,et al.  Weak maximum principle and accessory problem for control problems on time scales , 2009 .

[21]  Ravi P. Agarwal,et al.  Sturm-Liouville eigenvalue problems on time scales , 1999, Appl. Math. Comput..

[22]  Sturm–Liouville Problems on Time Scales with Separated Boundary Conditions , 2008 .

[23]  Werner Kratz,et al.  Oscillation theorems for symplectic difference systems , 2007 .

[24]  S. Hilger.  Analysis on Measure Chains — A Unified Approach to Continuous and Discrete Calculus , 1990 .