in this paper we apply the technique of measures of noncompactness to the theory of infinite system of integral equations in the fr´echet spaces. our aim is to provide a few generalization of tychonoff fixed point theorem and prove the existence of solutions for infinite systems of nonlinear integral equations with help of the technique of measures of noncompactness and a generalization of tych...

In the present paper, measure differential equations involving the distributional Henstock-Kurzweil integral are investigated. Theorems on the existence and structure of the set of solutions are established by using Schauder$^prime s$ fixed point theorem and Vidossich theorem. Two examples of the main results paper are presented. The new results are generalizations of some previous results in t...

I am a 22 yr old female grad student with fibromyalgia. I was officially diagnosed about 2 years ago, but have had it my whole life. I cannot find any record of children having it. I have seen lots of ads online for things to "cure" it but they are probably scams. I am struggling with how to deal with my illness. I am always tired, very depressed and anxious, ache, migraines, am very tense, res...

We show that if space is compact, then trajectories cannot be defined in the framework of the quantum Hamilton–Jacobi (HJ) equation. The starting point is the simple observation that when the energy is quantised it is not possible to make variations with respect to the energy, and the time parameterisation t − t0 = ∂ES0, implied by Jacobi’s theorem, which leads to the group velocity, is ill def...

Employing a three critical points theorem, we prove the existence ofmultiple solutions for a class of Neumann two-point boundary valueSturm-Liouville type equations. Using a local minimum theorem fordifferentiable functionals the existence of at least one non-trivialsolution is also ensured.

‎In this paper, based on [A. Razani, V. Rako$check{c}$evi$acute{c}$ and Z. Goodarzi, Nonself mappings in modular spaces and common fixed point theorems, Cent. Eur. J. Math. 2 (2010) 357-366.] a fixed point theorem for non-self contraction mapping $T$ in the modular space $X_rho$ is presented. Moreover, we study a new version of Krasnoseleskii's fixed point theorem for $S+T$, where $T$ is a cont...

The initial conditions of our universe appear to us in the form a classical probability distribution that we probe with cosmological observations. In current leading paradigm, this arises from quantum mechanical wavefunction universe. Here ask what imprint mechanics is on late time observables. We show requirement unitary evolution, colloquially conservation probabilities, fixes analytic struct...

In this paper we obtain a unique common xed point theorem for sixweakly compatible mappings in G-metric spaces.