Mediterranean Journal of Mathematics

In this paper, the authors establish the existence and uniqueness of solutions for a class of boundary value problem for nonlinear implicit fractional differential equations with impulses and Caputo–Hadamard type fractional derivatives. The stability of this problem is also studied. The arguments are based on the Banach contraction principle and Schaefer’s fixed point theorem. Two examples are presented to show the applicability of the results.

Let $${\mathcal{L}(X)}$$ be the algebra of all bounded linear operators on X and $${\mathcal{P}S(X)}$$ be the class of polaroid operators with the single-valued extension property. The property (gw) holds for $${T \in \mathcal{L}(X)}$$ if the complement in the approximate point spectrum of the semi-B-essential approximate point spectrum coincides with the set of all isolated points of the spectrum which are eigenvalues of the spectrum. In this note we focus on the stability of the property (gw) under perturbations: we prove that, if $${T \in \mathcal{P}S(X)}$$ and A (resp. Q) is an algebraic (resp. quasinilpotent) operator, then the property (gw) holds for f(T * + A *) (resp. f(T * + Q*)) for every analytic function f in σ(T + A) (resp. σ(T + Q)). Some applications are also given.

In this paper, we consider the curves on the surface in the unit 3-sphere. For a regular curve on a surface in the unit 3-sphere, we have a moving frame along the curve which is called a spherical Darboux frame. We induce two special vector fields along the curve with respect to the spherical Darboux frame and investigate the singularities of extrinsic flat great circular surfaces associated with these vector fields.

The present paper is devoted to study the curvature and torsion of slant Frenet curves in 3-dimensional normal almost paracontact metric manifolds. Moreover, in this class of manifolds, properties of non-Frenet slant curves (with null tangents or null normals) are studied. We illustrate such results by some examples.

In this paper, we develop a projection-type algorithm for set-valued variational inequalities on Hadamard manifolds. The proposed method is well defined whether the solution set of the problem is non-empty or not. Under pseudomonotonicity assumptions on the underlying vector field, our method is convergent to a solution of the given set-valued variational inequality. The results presented in this paper generalize and improve some known results introduced by Tang et al. (Optimization 64(5):1081–1096, 2015).

We provide results on the existence, non-existence, multiplicity, and localization of positive radial solutions for semilinear elliptic systems with Dirichlet or Robin boundary conditions on an annulus. Our approach is topological and relies on the classical fixed point index. We present an example to illustrate our theory.

In this paper, the water waves problem for uneven bottoms in a highly nonlinear regime is studied. It is well known that, for such regimes, a generalization of the Boussinesq equations called the Green–Naghdi equations can be derived and justified when the bottom is variable (Lannes and Bonneton in Phys Fluids 21, 2009). Moreover, the Green–Naghdi and Boussinesq equations are fully nonlinear and dispersive systems. We derive here new linear asymptotic models of the Green–Naghdi and Boussinesq equations so that they have the same accuracy as the standard equations. We solve explicitly the new linear models and numerically validate the results.

The notions of (metric) hypersurface data were introduced in Mars (Gen Relativ Gravit 45:2175–2221, 2013) as a tool to analyze, from an abstract viewpoint, hypersurfaces of arbitrary signature in pseudo-Riemannian manifolds. In this paper, general geometric properties of these notions are studied. In particular, the properties of the gauge group inherent to the geometric construction are analyzed and the metric hypersurface connection and its corresponding curvature tensor are studied. The results set up the stage for various potential applications. The particular but relevant case of spherical symmetry is considered in detail. In particular, a collection of gauge invariant quantities and a radial covariant derivative is introduced, such that the constraint equations of the Einstein field equations with matter can be written in a very compact form. The general solution of these equations in the vacuum case and Lorentzian ambient signature is obtained, and a generalization of the Birkhoff theorem to this abstract hypersurface setting is derived.

Let $${\mathcal {A}}$$ denote the class of analytic functions f in the unit disk $${\mathbb {D}}=\{z\in {\mathbb {C}}:|z|<1\}$$ normalized by $$f(0)=0$$ , $$f'(0)=1$$ . In the present article, we obtain the sharp estimates of the Schwarzian norm for functions in the classes $${\mathcal {G}}(\beta )=\{f\in {\mathcal {A}}:\mathrm{Re\,}[1+zf''(z)/f'(z)]<1+\beta /2\}$$ , where $$\beta >0$$ and $${\mathcal {F}}(\alpha )=\{f\in {\mathcal {A}}:\mathrm{Re\,}[1+zf''(z)/f'(z)]>\alpha \}$$ , where $$-1/2\le \alpha \le 0$$ . We also establish two-point distortion theorem for functions in the classes $${\mathcal {G}}(\beta )$$ and $${\mathcal {F}}(\alpha )$$ .