Explicit inhomogeneous Picard-Fuchs equations are obtained for Abelian integrals in piecewise smooth near-Hamiltonian systems, enabling recursive asymptotic expansions and bounds on the maximum number of isolated zeros of Melnikov functions near nilpotent saddle homoclinic loops.
Shi, An upper bound for the number of small-amplitude limit cycles in non- smooth Liénard system, Nonlinear Anal
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Inhomogeneous Picard-Fuchs equations of Abelian integrals in piecewise smooth near-Hamiltonian systems
Explicit inhomogeneous Picard-Fuchs equations are obtained for Abelian integrals in piecewise smooth near-Hamiltonian systems, enabling recursive asymptotic expansions and bounds on the maximum number of isolated zeros of Melnikov functions near nilpotent saddle homoclinic loops.