| dc.contributor.advisor | Koçak Fidan, Zeynep | |
| dc.contributor.author | Özpınar, Figen | |
| dc.date.accessioned | 2019-05-27T10:43:24Z | |
| dc.date.available | 2019-05-27T10:43:24Z | |
| dc.date.issued | 2009 | |
| dc.identifier.uri | http://hdl.handle.net/11630/6199 | |
| dc.description | In this study, consist of ve chapter. In the rst chapter, information about
oscillation of partial difference equations some studied before is given.
In the second chapter, some main topics of oscillation of difference equations and partial difference equations are given and some theorems and lemmas concerning these concepts also are reminded.
In the third chapter, necessary and suf cient conditions for the oscillation of the higher order linear partial difference equation with constant coef cient
1rm 1nh ym;n C . 1/r ChC1 pym ;n D 0
are obtained, where m; n; ; 2 N; r; h 2 N1, p is a nonnegative real number. The
forward partial differences 1m and 1n are de ned as usual, i.e.
1m Am;n D AmC1;n Am;n and 1n Am;n D Am;nC1 Am;n .
In the fourth chapter some oscillation criteria for the forced oscillation of a class of high order nonlinear partial difference equation
1rm 1nh ym;n C pm;n f .ym ;n / D qm;n
iv
are established, where m; n; ; 2 N; r; h 2 N1; pm;n and qm;n are double real
sequences de ned on N2; xf .x / > 0 for x 6D 0, which includes the special case
f .x/ D jxj sgnx for > 0. The forward partial differences 1m and 1n are
de ned as usual.
In the last chapter relations between the oscillation discrete nonlinear delay wave equations of the form
1n 2ym;n C pn 1n ym;n C qn f ym;n rn Lym;n D 0; 8 .m; n/ 2 • Nn0
and
1n 2ym;n C pn 1n ym;nC1 C qn f ym;n
rn Lym;n D 0; 8 .m; n/ 2 • Nn0
and the oscillation of their linear limiting equations are investigated, where M 2
Nn0 ; • D f1; 2;:::; Mg ; 2 N; fpn g ; fqn g ; frn g are sequences of real numbers, f
is continuous and convex, uf .u/ > 0 for u 6D 0 and Lym;n is the discrete Laplacian operator. | en_US |
| dc.description.abstract | Bu çal sma¸ be¸s bölümden olu¸smaktad r. Ilk bölümde k smi fark denklemlerinin
sal n ml l g ile ilgili yap lm s¸ baz çal smalar¸ hakk nda bilgi verilmi¸stir.
Ikinci bölümde fark denklemleri ve k smi fark denklemlerinin sal n ml l g ile ilgili temel bilgiler verilmi¸s olup, bunlara ili¸skin baz teorem ve lemmalar hat rlat lm st¸ r. Üçüncü bölümde
1rm 1nh ym;n C . 1/r ChC1 pym ;n D 0
yüksek mertebeden sabit katsay l lineer k smi fark denklemlerinin sal n ml l g için
gerek ve yeter ko¸sullar elde edilmi¸stir. Burada m; n; ; 2 N; r; h 2 N1 ve p
negatif olmayan bir reel say d r. 1m ve 1n bilindigi gibi tan ml k smi fark ope- ratörleridir.
Dördüncü bölümde
1rm 1nh ym;n C pm;n f .ym ;n / D qm;n
yüksek mertebeden lineer olmayan ikinci yanl k smi fark denklemlerinin sal n m- l l g için baz kriterler elde edilmi¸stir. Burada pm;n ve qm;n ; N2 üzerinde tan ml reel say lar n iki degi¸skenli dizileri, m; n; ; 2 N; r; h 2 N1; > 0 olmak üzere
f .x / D jx j sgnx özel durumunu içeren f fonksiyonu, x 6D 0 için xf .x / > 0 ko¸sulunu saglar. 1m ve 1n bilindigi gibi tan ml k smi fark operatörleridir.
ii
Son bölümde
1n 2ym;n C pn 1n ym;n C qn f ym;n
rn Lym;n D 0; 8 .m; n/ 2 • Nn0
ve
1n 2ym;n C pn 1n ym;nC1 C qn f ym;n
rn Lym;n D 0; 8 .m; n/ 2 • Nn0
lineer olmayan gecikmeli ayr k dalga denklemlerinin sal n ml l g ile bunlar n in- dirgenmi¸s lineer limit denklemlerinin sal n ml l g aras ndaki ili¸skiler ara¸st r lm st¸ r. Burada M 2 Nn0 ; • D f1; 2;:::; Mg ; 2 N; fpn g ; fqn g ve frn g reel say dizileri,
f sürekli fonksiyonu konveks ve x 6D 0 için xf .x / > 0 ve Lym;n , ayr k Laplace operatörüdür. | en_US |
| dc.language.iso | tur | en_US |
| dc.rights | info:eu-repo/semantics/openAccess | en_US |
| dc.subject | K smi Fark Denklemi, Sal n ml l k, Lineer Sal n ml l k, Dalga Denklemi, Yüksek Mertebeden K smi Fark Denklemi. | en_US |
| dc.title | Bazi Kismi Fark Denklemlerinin Salinimliligi Üzerine | en_US |
| dc.title.alternative | On The Oscillation Of Some Partial Difference Equations | en_US |
| dc.type | masterThesis | en_US |
| dc.department | Fen Bilimleri Enstitüsü | en_US |
| dc.identifier.startpage | 1 | en_US |
| dc.identifier.endpage | 79 | en_US |
| dc.relation.publicationcategory | Tez | en_US |
