We prove the following result: Let X be a real Hilbert space and let J: X → ℝ be a C¹ functional with a nonexpansive derivative. Then, for each r > 0, the following alternative holds: either J’ has a fixed point with norm less than r, or .
Using the ratio ergodic theorem for a measure preserving transformation in a -finite measure space we give a straightforward proof of Derriennic’s reverse maximal inequality for the supremum of ergodic ratios.
My recent book Antieigenvalue Analysis, World-Scientific, 2012, presented the theory of antieigenvalues from its inception in 1966 up to 2010, and its applications within those forty-five years to Numerical Analysis, Wavelets, Statistics, Quantum Mechanics, Finance, and Optimization. Here I am able to offer three further areas of application: Continuum Mechanics, Economics, and Number Theory. In particular, the critical angle of repose in a continuum model of granular materials is shown to be exactly...
MSC 2010: 34A37, 34B15, 26A33, 34C25, 34K37In this paper we prove the existence of solutions for fractional impulsive differential equations with antiperiodic boundary condition in Banach spaces. The results are obtained by using fractional calculus' techniques and the fixed point theorems.
In this paper we deal with the anti-periodic boundary value problems with nonlinearity of the form , where Extending to be multivalued we obtain the existence of solutions to hemivariational inequality and variational-hemivariational inequality.
The accretive operators theory is employed for proving an existence theorem for the evolutive energy equations involving simultaneously conduction, stationary convection (in the sense that the velocity field is assumed to be time independent), and radiation. In doing that we need to use new existence results for elliptic linear problems with mixed boundary conditions and irregular data.