Periodic solution of differential equation with ϕ-Laplacian and state-dependent impulses

On the Dirichlet problem in billiard spaces

“…The possible singularity lies in the state variable, and we overcome this obstacle by constructing the sequence of regular problems (9). By means of a priori bound technique and Arzelà-Ascoli Theorem we obtain the existence of multiple solutions of the two-point boundary value problem for singular equation (8).…”

“…Our next task is to prove the existence of a strictly monotone solution z of, possibly singular, equation (8).…”

“…Therefore z is strictly monotone. Now, it is sufficient to check that z is a solution to the differential equation (8). To do this, let us notice that, since all z i are strictly monotone, there are finite sets T i z = {t ∈ (0, T ) :…”

“…Among several interesting questions concerning the constraint system (2) there is one we would like to examine in the paper, the two-point boundary value problem with the boundary condition x(0) = A, x(T ) = B, where A, B ∈ K (comp., e.g., [6,7,8], where the two-point boundary value problem has been examined for time-and state-dependent impulses). It is very natural when we want to hit a ball to a hole.…”

La Φ-ecuación de Tricomi

“…, en procesamiento de señales [12], cuando φ(y) = |y|y p−1 con p > 1 o en modelos de epidemióloga con retraso [13], entre otras. En particular, son de interés los siguientes tipos de operadores:…”