We introduce a new variational method in order to derive results concerning existence and nodal properties of solutions to superlinear equations, and we focus on applications to the equation where h is a Caratheodory function which is odd in u. In the particular case where h is radially symmetric, we prove, for given n 2 N, the existence of a solution having precisely n nodal domains, whereas s...

The output time average of a discrete time single-input single-output nonlinear system is maximized in cyclic operation under constraints on the power of the periodic component of the control. The least upper bound is obtained by making use of the Caratheodory theorem on trigonometric moments. An algorithm to find a solution, optimal within any prescribed threshold is given, which reduces to st...

In this paper we prove the global bifurcation theorem for the nonlinear Picard problem. The right-hand side function φ is a Caratheodory map, not differentiable at zero, but behaving in the neighbourhood of zero as specified in details below. We prove that in some interval [a, b] ⊂ R the Leray-Schauder degree changes, hence there exists the global bifurcation branch. Later, by means of some app...

CR geometry originated from the study of real hypersurfaces in complex manifolds. In their foundational work Chern and Moser [CM] developed local invariants for CR manifolds. Shortly afterward Tanaka [T] and Webster [W2] introduced a canonical connection associated to a given pseudohermitian structure (i.e. a contact form), so pseudohermitian geometry was born. Today CR geometry or pseudohermit...

The Dependency Diagram of a Linear Programme (LP) shows how the successive inequalities of an LP depend on former inequalities, when variables are projected out by Fourier-Motzkin Elimination. It is also explained how redundant inequalities can be removed, using the method attributed to Chernikov and to Kohler. The procedure also leads to a transparent explanation of Farkas’Lemma, LP Duality, t...

by generalizing the well known guiding function method. Such an approach can be found in several works, however, under some heavier assumptions. For example, in [M] f is assumed to be locally lipschitzian and the guiding function to be C. In [GP] f needs to be of the Caratheodory type only, while the corresponding guiding function must be still C. In fact, in [GP] the more general, multivalued ...

In this article, we develop the distributed order fractional hybrid differential equations (DOFHDEs) with linear perturbations involving the fractional Riemann-Liouville derivative of order $0 < q < 1$ with respect to a nonnegative density function. Furthermore, an existence theorem for the fractional hybrid differential equations of distributed order is proved under the mixed $varphi$-Lipschit...