Existence results for functional and neutral functional integrodifferential inclusions with lower semicontinuous right-hand side

Abstract We study a boundary value problem associated to a fractional differential inclusion with “maxima”. Several existence results are obtained by using suitable fixed point theorems when the right hand side has convex or non convex values.

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Existence results for random impulsive neutral differential inclusions with lower semicontinuous

International Journal of Computing Science and Mathematics ◽

10.1504/ijcsm.2014.064066 ◽

2014 ◽

Vol 5 (2) ◽

pp. 151

Author(s):

A. Vinodkumar

Keyword(s):

Differential Inclusions ◽

Lower Semicontinuous ◽

Existence Results

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ON SOLUTIONS OF A DIFFERENTIAL INCLUSION WITH LOWER SEMICONTINUOUS NONCONVEX RIGHT-HAND SIDE IN A BANACH SPACE

Mathematics of the USSR-Sbornik ◽

10.1070/sm1986v053n01abeh002917 ◽

1986 ◽

Vol 53 (1) ◽

pp. 203-231 ◽

Cited By ~ 10

Author(s):

A A Tolstonogov ◽

I A Finogenko

Keyword(s):

Banach Space ◽

Differential Inclusion ◽

Lower Semicontinuous ◽

Right Hand

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Existence results for general inequality problems with constraints

Abstract and Applied Analysis ◽

10.1155/s1085337503210058 ◽

2003 ◽

Vol 2003 (10) ◽

pp. 601-619 ◽

Cited By ~ 2

Author(s):

George Dincă ◽

Petru Jebelean ◽

Dumitru Motreanu

Keyword(s):

Banach Space ◽

Lower Semicontinuous ◽

Directional Derivative ◽

Existence Results ◽

Laplacian Operator ◽

Hemivariational Inequalities ◽

General Inequality ◽

Locally Lipschitz ◽

Proper Convex ◽

Generalized Directional Derivative

This paper is concerned with existence results for inequality problems of typeF0(u;v)+Ψ′(u;v)≥0, for allv∈X, whereXis a Banach space,F:X→ℝis locally Lipschitz, andΨ:X→(−∞+∞]is proper, convex, and lower semicontinuous. HereF0stands for the generalized directional derivative ofFandΨ′denotes the directional derivative ofΨ. The applications we consider focus on the variational-hemivariational inequalities involving thep-Laplacian operator.

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Existence theorems for differential inclusions with nonconvex right hand side

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/s0161171286000595 ◽

1986 ◽

Vol 9 (3) ◽

pp. 459-469 ◽

Cited By ~ 4

Author(s):

Nikolaos S. Papageorgiou

Keyword(s):

Banach Space ◽

Separable Banach Space ◽

Differential Inclusions ◽

Existence Theorems ◽

Lower Semicontinuous ◽

Time Variable ◽

The State ◽

Infinite Dimensional ◽

State Variable ◽

Right Hand

In this paper we prove some new existence theorems for differential inclusions with a nonconvex right hand side, which is lower semicontinuous or continuous in the state variable, measurable in the time variable and takes values in a finite or infinite dimensional separable Banach space.

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Editorial Note

Journal of Speech Disorders ◽

10.1044/jshd.1101.02 ◽

1946 ◽

Vol 11 (1) ◽

pp. 2-2

Keyword(s):

Editorial Note ◽

Speech Sounds ◽

Left Hand ◽

Hand Column ◽

Right Hand ◽

Infant Speech ◽

The Right

In the article “Infant Speech Sounds and Intelligence” by Orvis C. Irwin and Han Piao Chen, in the December 1945 issue of the Journal, the paragraph which begins at the bottom of the left hand column on page 295 should have been placed immediately below the first paragraph at the top of the right hand column on page 296. To the authors we express our sincere apologies.

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Eosinophilic vasculitis: an inhabitual and resistant manifestation of a vasculitis

VASA ◽

10.1024/0301-1526/a000060 ◽

2010 ◽

Vol 39 (4) ◽

pp. 344-348 ◽

Cited By ~ 3

Author(s):

Jandus ◽

Bianda ◽

Alerci ◽

Gallino ◽

Marone

Keyword(s):

Skin Biopsy ◽

Intravenous Iron ◽

Small Vessel Vasculitis ◽

High Dose ◽

Raynaud Phenomenon ◽

The Third ◽

Left Elbow ◽

Right Hand ◽

The Right ◽

Trunk Skin

A 55-year-old woman was referred because of diffuse pruritic erythematous lesions and an ischemic process of the third finger of her right hand. She was known to have anaemia secondary to hypermenorrhea. She presented six months before admission with a cutaneous infiltration on the left cubital cavity after a paravenous leakage of intravenous iron substitution. She then reported a progressive pruritic erythematous swelling of her left arm and lower extremities and trunk. Skin biopsy of a lesion on the right leg revealed a fibrillar, small-vessel vasculitis containing many eosinophils.Two months later she reported Raynaud symptoms in both hands, with a persistent violaceous coloration of the skin and cold sensation of her third digit of the right hand. A round 1.5 cm well-delimited swelling on the medial site of the left elbow was noted. The third digit of her right hand was cold and of violet colour. Eosinophilia (19 % of total leucocytes) was present. Doppler-duplex arterial examination of the upper extremities showed an occlusion of the cubital artery down to the palmar arcade on the right arm. Selective angiography of the right subclavian and brachial arteries showed diffuse alteration of the blood flow in the cubital artery and hand, with fine collateral circulation in the carpal region. Neither secondary causes of hypereosinophilia nor a myeloproliferative process was found. Considering the skin biopsy results and having excluded other causes of eosinophilia, we assumed the diagnosis of an eosinophilic vasculitis. Treatment with tacrolimus and high dose steroids was started, the latter tapered within 12 months and then stopped, but a dramatic flare-up of the vasculitis with Raynaud phenomenon occurred. A new immunosupressive approach with steroids and methotrexate was then introduced. This case of aggressive eosinophilic vasculitis is difficult to classify into the usual forms of vasculitis and constitutes a therapeutic challenge given the resistance to current immunosuppressive regimens.

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