TY - JOUR
T1 - Numerical verification of existence and inclusion of solutions for nonlinear operator equations
AU - Oishi, Shin'ichi
PY - 1995/6/20
Y1 - 1995/6/20
N2 - Nonlinear operator equations of the type f(u) ≡ Lu + Nu = 0, u ∈ D(L) are considered, where L is a closed linear operator from a Banach space X to another Banach space Y and N a nonlinear operator from X to Y. A method is presented for numerical verification and inclusion of solutions for the equations. As an example, the existence of a periodic solution is proved for the Duffing equation.
AB - Nonlinear operator equations of the type f(u) ≡ Lu + Nu = 0, u ∈ D(L) are considered, where L is a closed linear operator from a Banach space X to another Banach space Y and N a nonlinear operator from X to Y. A method is presented for numerical verification and inclusion of solutions for the equations. As an example, the existence of a periodic solution is proved for the Duffing equation.
KW - Computer-assisted existence proof
KW - Duffing's equation
KW - Newton's method
KW - Self-validating numerics
KW - Urabe-Galerkin's method
UR - http://www.scopus.com/inward/record.url?scp=0003895707&partnerID=8YFLogxK
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U2 - 10.1016/0377-0427(94)00090-N
DO - 10.1016/0377-0427(94)00090-N
M3 - Article
AN - SCOPUS:0003895707
SN - 0377-0427
VL - 60
SP - 171
EP - 185
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
IS - 1-2
ER -