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Abstract

For r ∈ (1, 2], the authors establish sufficient conditions for the existence of solutions for a class of boundary value problem for rth 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

{-diva(x,u,u)=f,uW01Lϕ(Ω)L(Ω),

where a(x,s,ξ)ξϕ¯x-1(ϕ(x,h(|s|)))ϕ(x,|ξ|) and h : ℝ+→]0, 1] is a continuous decreasing function with unbounded primitive. The second term f belongs to LN(Ω) or to Lm(Ω), with m=rNr+1 for some r > 0 and φ is a Musielak function satisfying the Δ2-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

x˙=y-1(x)y,y˙=-x-f(x)-g(x)y-h(x)y2,

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 lk(x) has degree m and fk(x), gk(x) and hk(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

x(8)-(1+p2+λ2+μ2)x(6)+Ax+Bx¨+p2λ2μ2x=ɛF(t,x,x˙,x¨,x,x,x(5),x(6)x(7)),
where A = p 2λ2 + p 2 µ 2 + λ2 µ 2 + p 2 + λ2 + µ 2, B = p 2 λ2 + p 2 µ 2 + λ2 µ 2 + p 2λ2 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.