A Generalization of Picard's Method of Successive Approximation

1936 ◽  
Vol 32 (1) ◽  
pp. 86-95 ◽  
Author(s):  
H. O. Hirschfeld
Keyword(s):  
Differential Equation ◽  
Integral Equation ◽  
Boundary Value Problem ◽  
Linear Differential Equation ◽  
Successive Approximation ◽  
Linear Integral Equation ◽  
Non Linear ◽  
Linear Differential ◽  
Linear Integral ◽  
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It is well known that the boundary value problem for the non-linear differential equationcan be reduced with help of a Green's function K (x, ξ) to a non-linear integral equation of the type

Solutions of a non-linear differential equation. I

1967 ◽  
Vol 63 (3) ◽  
pp. 743-754 ◽  
Author(s):  
C. E. Billigheimer
Keyword(s):  
Differential Equation ◽  
Linear Differential Equation ◽  
Non Linear ◽  
Linear Differential ◽  
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We consider in this paper solutions of the equationwhere the primes indicate differentiation with respect to s, and a, b, c are constants.

scholarly journals Existence of limit cycles for a class of autonomous systems

1983 ◽  
Vol 28 (3) ◽  
pp. 331-337
Author(s):  
Anthony Sofo
Keyword(s):  
Differential Equation ◽  
Linear Differential Equation ◽  
Limit Cycle ◽  
Limit Cycles ◽  
Autonomous Systems ◽  
Non Linear ◽  
Stable Periodic ◽  
Linear Differential ◽  
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A proof is given for the existence of at least one stable periodic limit cycle solution for the polynomial non-linear differential equation of the formin some cases where the Levinson-Smith criteria are not directly applicable.

The existence of infinitely many solutions all bifurcating from λ = 0

1991 ◽  
Vol 118 (3-4) ◽  
pp. 295-303 ◽  
Author(s):  
Wolfgang Rother
Keyword(s):  
Differential Equation ◽  
Linear Differential Equation ◽  
Critical Point ◽  
Weak Solutions ◽  
Critical Point Theory ◽  
Point Theory ◽  
Infinitely Many Solutions ◽  
Non Linear ◽  
Linear Differential ◽  
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SynopsisWe consider the non-linear differential equationand state conditions for the function q such that (*) has infinitely many distinct pairs of (weak) solutions such that holds for all k ∈ ℕ. The main tools are results from critical point theory developed by A. Ambrosetti and P. H. Rabinowitz [1].

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