scholarly journals Measure Differential Inclusions: Existence Results and Minimum Problems

2020 ◽  
Author(s):  
Luisa Di Piazza ◽  
Valeria Marraffa ◽  
Bianca Satco
Keyword(s):  
Bounded Variation ◽  
Dynamic Systems ◽  
Differential Inclusions ◽  
Initial Point ◽  
Associated Solutions ◽  
Selection Principles ◽  
Measure Differential Inclusions ◽  
The Right ◽  
Nondecreasing Functions ◽  
Real Euclidean Space

Abstract We focus on a very general problem in the theory of dynamic systems, namely that of studying measure differential inclusions with varying measures. The multifunction on the right hand side has compact non-necessarily convex values in a real Euclidean space and satisfies bounded variation hypotheses with respect to the Pompeiu excess (and not to the Hausdorff-Pompeiu distance, as usually in literature). This is possible due to the use of interesting selection principles for excess bounded variation set-valued mappings. Conditions for the minimization of a generic functional with respect to a family of measures generated by equiregulated left-continuous, nondecreasing functions and to associated solutions of the differential inclusion driven by these measures are deduced, under constraints only on the initial point of the trajectory.

scholarly journals A decomposition of additive functionals of finite energy

1979 ◽  
Vol 74 ◽  
pp. 137-168 ◽  
Author(s):  
Masatoshi Fukushima
Keyword(s):  
Brownian Motion ◽  
Sobolev Space ◽  
Bounded Variation ◽  
Finite Energy ◽  
Signed Measure ◽  
Ito Formula ◽  
Tempered Distribution ◽  
Additive Functionals ◽  
Right Hand ◽  
The Right

The celebrated Ito formula for the n-dimensional Brownian motion Xt and for u ∈ C2(Rn) runs as follows:(0.1) In § 6 of this paper we extend this to the case where u is any element of the Sobolev space H1R(n) and accordingly Δu is a tempered distribution which is not even a signed measure in general. As a consequence the second term of the right hand side of (0.1) may not be of bounded variation in t.

The Effects of α-Viniferin on Adjuvant-Induced Arthritis in Rats

2004 ◽  
Vol 32 (04) ◽  
pp. 521-530 ◽  
Author(s):  
Jae Yeong Lee ◽  
Joong-Hyun Kim ◽  
Seong Soo Kang ◽  
Chun Sik Bae ◽  
Seok Hwa Choi
Keyword(s):  
Initial Point ◽  
Bone Destruction ◽  
Physiological Saline ◽  
Control Group ◽  
Sprague Dawley ◽  
Mineral Density ◽  
Entire Study ◽  
Adjuvant Induced Arthritis ◽  
Radiological Changes ◽  
The Right

This study was performed to assess the efficacy of α-viniferin (Carex humilis Leyss) on adjuvant-induced arthritis in rats. Adjuvant arthritis was induced by a single subcutaneous injection of 0.1 ml complete Freund's adjuvant (CFA) containing 7.5 mg Mycobacterium butyricum suspended in 1 ml sterile paraffin oil into the right hind paw. Forty female Sprague-Dawley rats were injected. Righting reflex was uniformly lost and considered to be the initial point of arthritis development on day 7 after CFA injection. Rats were divided into four groups, and upon development of arthritis, tested groups were orally administered 3 or 10 mg/kg α-viniferin or 10 mg/kg ketoprofen every day for 14 days. The control group was orally administered 2 ml of physiological saline solution. Bone mineral density (BMD), radiological changes and edematous volumes were measured for 35 days. α-viniferin suppressed the development of inflammatory edema, and inhibited the bone destruction, noted with a decrease in BMD ( p <0.05). Hind paw edema volume, BMD and radiological changes did not differ significantly in the ketoprofen and α-viniferin groups during the entire study period. In conclusion, α-viniferin suppressed arthritic inflammation and bony change in rats.

scholarly journals Existence results of nonlinear generalized proportional fractional differential inclusions via the diagonalization technique

2021 ◽  
Vol 6 (11) ◽  
pp. 12832-12844
Author(s):  
Mohamed I. Abbas ◽  
◽  
Snezhana Hristova ◽  
Keyword(s):  
Differential Inclusions ◽  
Existence Of Solutions ◽  
Existence Results ◽  
Inclusion Problem ◽  
Fractional Differential Inclusions ◽  
New Class ◽  
Nonlinear Alternative ◽  
Fractional Differential ◽  
Infinite Intervals ◽  
The Right

<abstract><p>The present paper is concerned with the existence of solutions of a new class of nonlinear generalized proportional fractional differential inclusions with the right-hand side contains a Carathèodory-type multi-valued nonlinearity on infinite intervals. The investigation of the proposed inclusion problem relies on the multi-valued form of Leray-Schauder nonlinear alternative incorporated with the diagonalization technique. By specializing the parameters involved in the problem at hand, an illustrated example is proposed.</p></abstract>

scholarly journals Stieltjes Differential Inclusions with Periodic Boundary Conditions without Upper Semicontinuity

Mathematics ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 55
Author(s):  
Valeria Marraffa ◽  
Bianca Satco
Keyword(s):  
Boundary Conditions ◽  
Differential Inclusions ◽  
Periodic Boundary ◽  
Existence Of Solutions ◽  
Compact Convex ◽  
Upper Semicontinuity ◽  
Periodic Boundary Conditions ◽  
Set Valued Mapping ◽  
Periodic Problems ◽  
The Right

We are studying first order differential inclusions with periodic boundary conditions where the Stieltjes derivative with respect to a left-continuous non-decreasing function replaces the classical derivative. The involved set-valued mapping is not assumed to have compact and convex values, nor to be upper semicontinuous concerning the second argument everywhere, as in other related works. A condition involving the contingent derivative relative to the non-decreasing function (recently introduced and applied to initial value problems by R.L. Pouso, I.M. Marquez Albes, and J. Rodriguez-Lopez) is imposed on the set where the upper semicontinuity and the assumption to have compact convex values fail. Based on previously obtained results for periodic problems in the single-valued cases, the existence of solutions is proven. It is also pointed out that the solution set is compact in the uniform convergence topology. In particular, the existence results are obtained for periodic impulsive differential inclusions (with multivalued impulsive maps and finite or possibly countable impulsive moments) without upper semicontinuity assumptions on the right-hand side, and also the existence of solutions is derived for dynamic inclusions on time scales with periodic boundary conditions.

scholarly journals On controllability for a class of second-order differential inclusions

2011 ◽  
Vol 27 (1) ◽  
pp. 34-40
Author(s):  
AURELIAN CERNEA ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Inclusion ◽  
Point Theorem ◽  
Differential Inclusions ◽  
Second Order ◽  
Sufficient Condition ◽  
Liouville Type ◽  
Sturm Liouville ◽  
The Right

By using a suitable fixed point theorem a sufficient condition for controllability is obtained for a Sturm-Liouville type differential inclusion in the case when the right hand side has convex values.

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