## Abstract

For *r* ∈ (1, 2], the authors establish sufficient conditions for the existence of solutions for a class of boundary value problem for *r*th order Caputo-Hadamard fractional differential inclusions satisfying nonlinear integral conditions. Both cases of convex and nonconvex valued right hand sides are considered.

## Abstract

In this paper, we show the existence of solutions for the nonlinear elliptic equations of the form

where *h* : ℝ+→]0, 1] is a continuous decreasing function with unbounded primitive. The second term *f* belongs to *L ^{N}*(Ω) or to

*L*(Ω), with

^{m}*r*> 0 and

*φ*is a Musielak function satisfying the Δ

_{2}-condition.

## Abstract

In this paper, we discuss the hypercyclic properties of composition operators on Orlicz function spaces. We give some different conditions under which a composition operator on Orlicz spaces is hyper-cyclic or not. Similarly, multiplication operators are considered. It is shown that there is no hypercyclic multiplication operator on Orlicz spaces.

## Abstract

Via Leray-Schauder’s nonlinear alternative, we obtain the existence of a weak solution for a nonlocal problem driven by an operator of elliptic type in a fractional Orlicz-Sobolev space, with homogeneous Dirichlet boundary conditions.

## Abstract

We apply the averaging theory of first and second order for studying the limit cycles of generalized polynomial Linard systems of the form

where *l*(*x*) = *∊l*
_{1}(*x*) + *∊*
^{2}
*l*
_{2}(*x*), *f* (*x*) = *∊ f*
_{1}(*x*) + *∊*
^{2}
*f*
_{2}(*x*), *g*(*x*) = *∊g*
_{1}(*x*) + *∊*
^{2}
*g*
_{2}(*x*) and *h*(*x*) = *∊h*
_{1}(*x*) + *∊*
^{2}
*h*
_{2}(*x*) where *l _{k}*(

*x*) has degree

*m*and

*f*(

_{k}*x*),

*g*(

_{k}*x*) and

*h*(

_{k}*x*) have degree

*n*for each

*k*= 1, 2, and

*∊*is a small parameter.

## Abstract

In this paper, we introduce the notion of (*q*, *p*)-mixing operators from the injective tensor product space *E* ̂⊗_{∈}
*F* into a Banach space *G* which we call (*q*, *p*, *F*)-mixing. In particular, we extend the notion of (*q*, *p*, *E*)-summing operators which is a special case of (*q*, *p*, *F*)-mixing operators to Lipschitz case by studying their properties and showing some results for this notion.

## Abstract

In this paper, we continue studying the properties of weak soft axioms discussed and studied in [8]. We initiate and explore soft semi-*R*
_{0} spaces at soft point in terms of soft semi-open sets and study its characterizations and properties. It is interesting to mention that this soft contains the soft semi-closure of each of its soft point singletons. We also define soft semi-*R*
_{1} spaces at soft point and discuss some of its characterizations.

## Abstract

We prove the existence of renormalized solutions to a class of nonlinear evolution equations, supplemented with initial and Dirichlet condition in the framework of generalized Sobolev spaces. The data are assumed merely integrable.

## Abstract

In this article, we provide sufficient conditions for the existence of periodic solutions of the eighth-order differential equation

*A*=

*p*

^{2}λ

^{2}+

*p*

^{2}

*µ*

^{2}+ λ

^{2}

*µ*

^{2}+

*p*

^{2}+ λ

^{2}+

*µ*

^{2},

*B*=

*p*

^{2}λ

^{2}+

*p*

^{2}

*µ*

^{2}+ λ

^{2}

*µ*

^{2}+

*p*

^{2}λ

^{2}

*µ*

^{2}, with λ,

*µ*and

*p*are rational numbers different from −1, 0, 1, and

*p*≠ ±λ,

*p*≠±

*µ*, λ ≠±

*µ*, ɛ is sufficiently small and

*F*is a nonlinear non-autonomous periodic function. Moreover we provide some applications.

## Abstract

In this work, we establish some new (*k*, *s*) −fractional integral inequalities of continuous random variables by using the (*k*, *s*) −Riemann-Liouville fractional integral operator.