# On oscillatory first order nonlinear neutral differential equations with nonlinear impulses

Ontology type: schema:ScholarlyArticle

### Article Info

DATE

2018-03-16

AUTHORS ABSTRACT

In this work, we study the oscillatory behaviour of solutions of a class of first order impulsive neutral delay differential equations of the form (y(t)-p(t)y(t-τ))′+q(t)G(y(t-σ))=0,t≠tk,t≥t0y(tk+)=Ik(y(tk)),k∈Ny(tk+-τ)=Ik(y(tk-τ)),k∈N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\begin{aligned} {\left\{ \begin{array}{ll} \bigl (y(t)-p(t)y(t-\tau )\bigr )' + q(t)G\bigl (y(t-\sigma )\bigr )=0,\;t\ne t_k,\;t \ge t_0 \\ y(t^+_k)=I_k\bigl (y(t_k)\bigr ), \;k \in {\mathbb {N}} \\ y(t^+_k-\tau )=I_k\bigl (y(t_k-\tau )\bigr ), \;k \in {\mathbb {N}} \end{array}\right. } \end{aligned}\end{document}for different ranges of the neutral coefficient p. Finally, two illustrative examples are included to show the effectiveness and feasibility of the main results. More... »

PAGES

257-270

### Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s12190-018-1178-8

DOI

http://dx.doi.org/10.1007/s12190-018-1178-8

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1101556273

Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
Incoming Citations Browse incoming citations for this publication using opencitations.net

JSON-LD is the canonical representation for SciGraph data.

TIP: You can open this SciGraph record using an external JSON-LD service:

[
{
"@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json",
{
"id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/01",
"inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/",
"name": "Mathematical Sciences",
"type": "DefinedTerm"
},
{
"id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0101",
"inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/",
"name": "Pure Mathematics",
"type": "DefinedTerm"
}
],
"author": [
{
"affiliation": {
"alternateName": "Department of Mathematics, Sambalpur University, 768019, Sambalpur, India",
"id": "http://www.grid.ac/institutes/grid.444716.4",
"name": [
"Department of Mathematics, Sambalpur University, 768019, Sambalpur, India"
],
"type": "Organization"
},
"familyName": "Santra",
"givenName": "Shyam S.",
"id": "sg:person.013610455004.25",
"sameAs": [
"https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013610455004.25"
],
"type": "Person"
},
{
"affiliation": {
"alternateName": "Department of Mathematics, Sambalpur University, 768019, Sambalpur, India",
"id": "http://www.grid.ac/institutes/grid.444716.4",
"name": [
"Department of Mathematics, Sambalpur University, 768019, Sambalpur, India"
],
"type": "Organization"
},
"familyName": "Tripathy",
"givenName": "Arun K.",
"id": "sg:person.012376513600.76",
"sameAs": [
"https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012376513600.76"
],
"type": "Person"
}
],
"citation": [
{
"id": "sg:pub.10.1007/978-1-4612-9892-2",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1021421011",
"https://doi.org/10.1007/978-1-4612-9892-2"
],
"type": "CreativeWork"
}
],
"datePublished": "2018-03-16",
"datePublishedReg": "2018-03-16",
"description": "In this work, we study the oscillatory behaviour of solutions of a class of first order impulsive neutral delay differential equations of the form (y(t)-p(t)y(t-\u03c4))\u2032+q(t)G(y(t-\u03c3))=0,t\u2260tk,t\u2265t0y(tk+)=Ik(y(tk)),k\u2208Ny(tk+-\u03c4)=Ik(y(tk-\u03c4)),k\u2208N\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}\\begin{aligned} {\\left\\{ \\begin{array}{ll} \\bigl (y(t)-p(t)y(t-\\tau )\\bigr )' + q(t)G\\bigl (y(t-\\sigma )\\bigr )=0,\\;t\\ne t_k,\\;t \\ge t_0 \\\\ y(t^+_k)=I_k\\bigl (y(t_k)\\bigr ), \\;k \\in {\\mathbb {N}} \\\\ y(t^+_k-\\tau )=I_k\\bigl (y(t_k-\\tau )\\bigr ), \\;k \\in {\\mathbb {N}} \\end{array}\\right. } \\end{aligned}\\end{document}for different ranges of the neutral coefficient p. Finally, two illustrative examples are included to show the effectiveness and feasibility of the main results.",
"genre": "article",
"id": "sg:pub.10.1007/s12190-018-1178-8",
"inLanguage": "en",
"isAccessibleForFree": false,
"isPartOf": [
{
"id": "sg:journal.1136398",
"issn": [
"1598-5865",
"1865-2085"
],
"name": "Journal of Applied Mathematics and Computing",
"publisher": "Springer Nature",
"type": "Periodical"
},
{
"issueNumber": "1-2",
"type": "PublicationIssue"
},
{
"type": "PublicationVolume",
}
],
"keywords": [
"main results",
"p.",
"differential equations",
"neutral delay differential equations",
"delay differential equations",
"neutral differential equations",
"impulses",
"effectiveness",
"feasibility",
"nonlinear impulses",
"results",
"illustrative example",
"form",
"equations",
"oscillatory behavior",
"first order",
"range",
"class",
"different ranges",
"behavior",
"order",
"solution",
"work",
"example",
"first order impulsive neutral delay differential equations",
"order impulsive neutral delay differential equations",
"impulsive neutral delay differential equations",
"neutral coefficient p.",
"coefficient p.",
"oscillatory first order"
],
"name": "On oscillatory first order nonlinear neutral differential equations with nonlinear impulses",
"pagination": "257-270",
"productId": [
{
"name": "dimensions_id",
"type": "PropertyValue",
"value": [
"pub.1101556273"
]
},
{
"name": "doi",
"type": "PropertyValue",
"value": [
"10.1007/s12190-018-1178-8"
]
}
],
"sameAs": [
"https://doi.org/10.1007/s12190-018-1178-8",
"https://app.dimensions.ai/details/publication/pub.1101556273"
],
"sdDataset": "articles",
"sdDatePublished": "2021-12-01T19:40",
"sdPublisher": {
"name": "Springer Nature - SN SciGraph project",
"type": "Organization"
},
"sdSource": "s3://com-springernature-scigraph/baseset/20211201/entities/gbq_results/article/article_769.jsonl",
"type": "ScholarlyArticle",
"url": "https://doi.org/10.1007/s12190-018-1178-8"
}
]

HOW TO GET THIS DATA PROGRAMMATICALLY:

JSON-LD is a popular format for linked data which is fully compatible with JSON.

curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/s12190-018-1178-8'

N-Triples is a line-based linked data format ideal for batch operations.

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/s12190-018-1178-8'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s12190-018-1178-8'

RDF/XML is a standard XML format for linked data.

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s12190-018-1178-8'

This table displays all metadata directly associated to this object as RDF triples.

99 TRIPLES      22 PREDICATES      56 URIs      47 LITERALS      6 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/s12190-018-1178-8 schema:about anzsrc-for:01
2 anzsrc-for:0101
3 schema:author N60ca008233d64afe9d690d7771480465
4 schema:citation sg:pub.10.1007/978-1-4612-9892-2
5 schema:datePublished 2018-03-16
6 schema:datePublishedReg 2018-03-16
7 schema:description In this work, we study the oscillatory behaviour of solutions of a class of first order impulsive neutral delay differential equations of the form (y(t)-p(t)y(t-τ))′+q(t)G(y(t-σ))=0,t≠tk,t≥t0y(tk+)=Ik(y(tk)),k∈Ny(tk+-τ)=Ik(y(tk-τ)),k∈N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\begin{aligned} {\left\{ \begin{array}{ll} \bigl (y(t)-p(t)y(t-\tau )\bigr )' + q(t)G\bigl (y(t-\sigma )\bigr )=0,\;t\ne t_k,\;t \ge t_0 \\ y(t^+_k)=I_k\bigl (y(t_k)\bigr ), \;k \in {\mathbb {N}} \\ y(t^+_k-\tau )=I_k\bigl (y(t_k-\tau )\bigr ), \;k \in {\mathbb {N}} \end{array}\right. } \end{aligned}\end{document}for different ranges of the neutral coefficient p. Finally, two illustrative examples are included to show the effectiveness and feasibility of the main results.
8 schema:genre article
9 schema:inLanguage en
10 schema:isAccessibleForFree false
11 schema:isPartOf N2418b509b21f42458016e962d6e10724
12 Nee9d1638c08a4c1dbdd54ef9c135816b
13 sg:journal.1136398
14 schema:keywords behavior
15 class
16 coefficient p.
17 delay differential equations
18 different ranges
19 differential equations
20 effectiveness
21 equations
22 example
23 feasibility
24 first order
25 first order impulsive neutral delay differential equations
26 form
27 illustrative example
28 impulses
29 impulsive neutral delay differential equations
30 main results
31 neutral coefficient p.
32 neutral delay differential equations
33 neutral differential equations
34 nonlinear impulses
35 order
36 order impulsive neutral delay differential equations
37 oscillatory behavior
38 oscillatory first order
39 p.
40 range
41 results
42 solution
43 work
44 schema:name On oscillatory first order nonlinear neutral differential equations with nonlinear impulses
45 schema:pagination 257-270
46 schema:productId N5b4653753a914b888a132bac7811be83
47 N75b21a0e6a5c432e8e0c9dfb2516882b
48 schema:sameAs https://app.dimensions.ai/details/publication/pub.1101556273
49 https://doi.org/10.1007/s12190-018-1178-8
50 schema:sdDatePublished 2021-12-01T19:40
52 schema:sdPublisher Ned1d6f8c6bdf45f394ced4415f3baedb
53 schema:url https://doi.org/10.1007/s12190-018-1178-8
55 sgo:sdDataset articles
56 rdf:type schema:ScholarlyArticle
57 N2418b509b21f42458016e962d6e10724 schema:volumeNumber 59
58 rdf:type schema:PublicationVolume
59 N5b4653753a914b888a132bac7811be83 schema:name doi
60 schema:value 10.1007/s12190-018-1178-8
61 rdf:type schema:PropertyValue
62 N60ca008233d64afe9d690d7771480465 rdf:first sg:person.013610455004.25
63 rdf:rest Nff37b372691341ab80968ff047338245
64 N75b21a0e6a5c432e8e0c9dfb2516882b schema:name dimensions_id
65 schema:value pub.1101556273
66 rdf:type schema:PropertyValue
67 Ned1d6f8c6bdf45f394ced4415f3baedb schema:name Springer Nature - SN SciGraph project
68 rdf:type schema:Organization
69 Nee9d1638c08a4c1dbdd54ef9c135816b schema:issueNumber 1-2
70 rdf:type schema:PublicationIssue
71 Nff37b372691341ab80968ff047338245 rdf:first sg:person.012376513600.76
72 rdf:rest rdf:nil
73 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
74 schema:name Mathematical Sciences
75 rdf:type schema:DefinedTerm
76 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
77 schema:name Pure Mathematics
78 rdf:type schema:DefinedTerm
79 sg:journal.1136398 schema:issn 1598-5865
80 1865-2085
81 schema:name Journal of Applied Mathematics and Computing
82 schema:publisher Springer Nature
83 rdf:type schema:Periodical
84 sg:person.012376513600.76 schema:affiliation grid-institutes:grid.444716.4
85 schema:familyName Tripathy
86 schema:givenName Arun K.
87 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012376513600.76
88 rdf:type schema:Person
89 sg:person.013610455004.25 schema:affiliation grid-institutes:grid.444716.4
90 schema:familyName Santra
91 schema:givenName Shyam S.
92 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013610455004.25
93 rdf:type schema:Person
94 sg:pub.10.1007/978-1-4612-9892-2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1021421011
95 https://doi.org/10.1007/978-1-4612-9892-2
96 rdf:type schema:CreativeWork
97 grid-institutes:grid.444716.4 schema:alternateName Department of Mathematics, Sambalpur University, 768019, Sambalpur, India
98 schema:name Department of Mathematics, Sambalpur University, 768019, Sambalpur, India
99 rdf:type schema:Organization

Preview window. Press ESC to close (or click here)

...