Although shockingly little research has been devoted to differential care (because genes were largely assumed to explain sibling difference), it is established that two-thirds of children claim that their parents show some form of preferential treatment.
More recently, a certain interest has been devoted to differential operators involving also a nonlinear function of the state variable as in the following equation: bigl(a bigl(x t) bigr)Phibigl(x'(t) bigr) bigr)'= f bigl t,x t),x'(t) bigr), quadtext{a.e. in } I=[0,T], (1) where a is a continuous positive function, ϕ is a strictly increasing homeomorphism and f is a Carathéodory function.
However, to the best of our knowledge, little literatures has been devoted to measure differential equations in infinite-dimensional spaces except [1] and [26, 27].
Much attention has been devoted to the fractional differential inclusions (see for example, [16 32] and the references therein).
Many articles have been devoted to the study of differential equations of the type ( ( Φ ( x ′ ) ) ′ ( t ) = f ( t, x ( t ), x ′ ( t ) ). for Φ-Laplacian operators, and recently also the study of singular or non-surjective differential operators has become object of an increasing interest (see, i.e., [1 10]).
During the past few decades, fractional differential equations have proved to be valuable tools in the modeling of many phenomena in viscoelasticity, electrochemistry, control, porous media, and electromagnetism, etc. Due to its tremendous scopes and applications, several monographs have been devoted to the study of fractional differential equations; see the monographs [1 5].
On the other hand, we remark that a great deal of research has been devoted to the extension of a differential operator like (1.6) to the infinitesimal generator of a diffusion semigroup in the space L p ( H, ν ), p ≥ 1, where ν is an invariant measure for the semigroup (see, for example, [7 11] and references therein).
In the past years, much attention has been devoted to the study of fractional differential equations due to the fact that they have many applications in a broad range of areas such as physics, chemistry, aerodynamics, electrodynamics of complex medium and polymer rheology.
Several papers have been devoted to the study of third order differential equations with two-point and three-point boundary conditions.
A wide literature has been devoted to the study of boundary value problems for differential equations involving various types of nonlinear differential operators.
Recently, many efforts have been devoted to the study of chaotic dynamics of variable-order differential systems [23 28].
