Qualitative analysis of the Cauchy problem \(F(t,x,x')=0, x(0)=0\)

DOI10.1007/s10958-007-0347-3zbMath1158.34303OpenAlexW2061046923MaRDI QIDQ941999

Yu. V. Kuzina, Alexander E. Zernov

Publication date: 3 September 2008

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-007-0347-3

zbMATH Keywords

initial value problemsasymptoticimplicit equations

Mathematics Subject Classification ID

Implicit ordinary differential equations, differential-algebraic equations (34A09) Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations (34A12)

Cites Work

• Sulla risoluzione dell'equazione \(F(t, x, dx/dt) = 0\)
• Actions with a finite number of orbits
• On a singular problem of Cauchy-Nicoletti
• Boundary value problems for systems of implicit differential equations
• Qualitative analysis of the singular Cauchy problem for a differential equation unsolved for the derivative
• Improper singular points of corank 1 of systems of differential equations not solved for the derivatives
• On proper singular points of ordinary differential equations unsolved for derivatives
• A difference method of solving the differential equation y' = h(t, y, y, y')
• Implicit differential equations and vector fields with non-isolated singular points
• Existence and Asymptotic Behavior of Solutions of the Cauchy Problem x (x′) = f(t, x, x′), x(0) = 0
• The polygonal method of solving the differential equation y' = h(t, y, y, y')
• Qualitative Investigation of the Singular Cauchy Problem F(t, x, x ) = 0, x(0) = 0
• Boundary value problems for implicit ODE's in a singular case
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