Nonlinear systems with singular vectorϕ-Laplacian under the Hartman-type condition

Rotating periodic solutions for second order systems with Hartman-type nonlinearity

“…In [4], Mawhin applied the Schauder fixed point theorem to obtain periodic solutions of p-Laplacian ordinary differential systems under assumption (H). In [5,6], some results are obtained on periodic solutions of ordinary differential systems involving singular φ-Laplace operator and φ(t)-Laplace operator under the Hartman-type condition (H). For some variants and extensions, one can see [7][8][9][10][11] and the references therein.…”

An application of coincidence degree theory to cyclic feedback type systems associated with nonlinear differential operators

“…with γ(s) a positive continuous function defined for s > 0. Such class of operators is clearly included in that of the form (5.7) and it has been considered in [13] for the singular case, namely for φ defined on an open ball B(0, a) and, consequently, for γ(s) with 0 < s < a < +∞.…”

“…The homeomorphism defined in (5.11) is a special case of a class of maps of the formφ(ξ) := γ(|ξ|)ξ, if ξ ∈ R m \ {0}, φ(0) = 0,(5.12)with γ(s) a positive continuous function defined for s > 0. Such class of operators is clearly included in that of the form (5.7) and it has been considered in[13] for the singular case, namely for φ defined on an open ball B(0, a) and, consequently, for γ(s) with 0 < s < a < +∞. A natural question which raises in this context is whether the homeomorphisms φ of the form (5.7) (and thus, in particular, (5.12)) belong to the class of nonlinear operators introduced by Manásevich and Mawhin in[16] and satisfying conditions (H1) and (H2) recalled in Remark 3.2.…”