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Further extension of the Levinson transformation theory is performed for partially dissipative periodic processes via the fixed point index. Thus, for example, the periodic problem for differential inclusions can be treated by means of the multivalued Poincaré translation operator. In a certain case, the well-known Ważewski principle can also be generalized in this way, because no transversality is required on the boundary.

Period doubling bifurcations in a two-box model of the Brusselator

Alois Klíč (1983)

Aplikace matematiky

Two theorems about period doubling bifurcations are proved. A special case, where one multiplier of the homogeneous solution is equal to +1 is discussed in the Appendix.

Period-doublings and orbit-bifurcations in symmetric systems

A. Vanderbauwhede (1989)

Banach Center Publications

Periodic and almost periodic solutions for multi-valued differential equations in Banach spaces.

Hanebaly, E., Marzouki, B. (2000)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Periodic and aqlmost-periodic solutions of semihnear equations in Banach spaces.

M. BAHAJ AND E. HANEBALY (1999)

Revista de la Real Academia de Ciencias Exactas Físicas y Naturales

Periodic and heteroclinic orbits for a periodic hamiltonian system

Paul H. Rabinowitz (1989)

Annales de l'I.H.P. Analyse non linéaire

Periodic bounce trajectories with a low number of bounce points

V. Benci, F. Giannoni (1989)

Annales de l'I.H.P. Analyse non linéaire

Periodic boundary value problem for certain nonlinear differential equations of the third order

Ján Andres (1985)

Mathematica Slovaca

Periodic boundary value problem in Hilbert space for differential equation of second order with reflection of the argument

Boris Rudolf (1992)

Mathematica Slovaca

Periodic boundary value problem of a fourth order differential inclusion

Marko Švec (1997)

Archivum Mathematicum

The paper deals with the periodic boundary value problem (1) $L_{4} x (t) + a (t) x (t) \in F (t, x (t))$ , $t \in J = [a, b]$ , (2) $L_{i} x (a) = L_{i} x (b)$ , $i = 0, 1, 2, 3$ , where $L_{0} x (t) = a_{0} x (t)$ , $L_{i} x (t) = a_{i} (t) L_{i - 1} x (t)$ , $i = 1, 2, 3, 4$ , $a_{0} (t) = a_{4} (t) = 1$ , $a_{i} (t)$ , $i = 1, 2, 3$ and $a (t)$ are continuous on $J$ , $a (t) \geq 0$ , $a_{i} (t) > 0$ , $i = 1, 2$ , $a_{1} (t) = a_{3} (t) \cdot F (t, x) : J \times R \to$ {nonempty convex compact subsets of $R$ }, $R = (- \infty, \infty)$ . The existence of such periodic solution is proven via Ky Fan’s fixed point theorem.

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Optimal conditions for maximum and antimaximum principles of the periodic solution problem.

Optimal impulsive harvest policy for time-dependent logistic equation with periodic coefficients.

Orbites périodiques des systèmes hamiltoniens du type de celui des trois corps

Orbites périodiques d'un système hamiltonien du voisinage d'un point d'équilibre

Oscillating rivers. (Fleuves oscillants.)

Oscillations de systèmes hamiltoniens non linéaires. III

Oscillations forcées de systèmes hamiltoniens non linéaires

Partially dissipative periodic processes