... subsets O1 and O2, where O1is bounded and O2is unbounded and we get the conclusion of this theorem for Γ, O1, and O2.4. MultiplicityIn this section, we study existence of the second positive ... a completely continuoussuch that eitheri Tu≤u for u ∈K∩∂Ω1 and Tu≥u for u ∈K∩∂Ω2orii Tu≥u for u ∈K∩∂Ω1 and Tu≤u for u ∈K∩∂Ω2.Then T has a fixed point in K∩Ω2\ ... O0,1\O ∪ Γ0, and no solution for λ, μ ∈O0,2.If ki: l1,l2 → 0, ∞ are continuous andsingular at r l1 and/ or l2, then hiare also singular at t 0 and/ or 1. In this case, we...
... 304601-925-7289writingcenter@mc.eduRules for Forming Plural Nouns To form the plural of nouns, follow the rules below. 1. Add s to most nouns. girl/girls bicycle/bicycles printer/printers 2. Add es to nouns ending is ... buzz/buzzes church/churches wish/wishes 3. Fornouns ending in y preceded by a consonant, change y to i and add es. fly/flies party/parties daisy/daisies 4. Fornouns ending in y preceded by a vowel, ... valley/valleys 5. Fornouns ending in o preceded by a consonant, add es. hero/heroes potato/potatoes 6. Fornouns ending in o preceded by a vowel, add s. Oreo/Oreos radio/radios patio/patios 7. For musical...
... ArticleSolutions and Green’s Functions for Boundary Value Problems of Second- OrderFour-Point Functional Difference EquationsYang Shujie and Shi BaoInstitute of Systems Science and Mathematics, ... BVPs of differential and difference equationshave been studied widely and there are many excellent results see Gai et al. 1, Guo and Tian 2, Henderson and Peterson 3, and Yang et al. 4. ... Science Foundation of Naval Aeronautical and AstronauticalUniversity.References1 M. J. Gai, B. Shi, and D. C. Zhang, “Boundary value problems for second- order singular functionaldifferential equations,”...
... well defined and is continuous and completely continuous. Next weclaim that:i Tx≤x for x ∈ ∂KΩ1, and ii there exists υ ∈ K \{0} such that x/ Tx λυ for all x ∈ ∂KΩ2 and all λ>0.14 ... differences betweena strong singularity and a weak singularity.Boundary Value Problems 198 P. Yan and M. Zhang, “Higher order non-resonance for differential equations with singularities,”Mathematical ... “Forced singular oscillators and the method of lower and uppersolutions,” Topological Methods in Nonlinear Analysis, vol. 22, no. 2, pp. 297–317, 2003.30 P. Habets and F. Zanolin, “Upper and...
... standardtopology on R and say t is right scattered, left scattered, right dense and left dense if σt >t, ρt <t,σtt, and ρtt, respectively. Finally, we introduce the sets Tk and ... ArticleNecessary and Sufficient Conditions for the Existence of Positive Solution for Singular Boundary Value Problems on Time ScalesMeiqiang Feng,1Xuemei Zhang,2, 3Xianggui Li,1 and Weigao Ge31School ... 1Tpositive solutions for a class of singular boundary value problems on time scales. The results significantly extend and improve manyknown results for both the continuous case and more general time...
... ArticleExistence and Uniqueness of Solutions for Singular Higher Order Continuous and DiscreteBoundary Value ProblemsChengjun Yuan,1, 2Daqing Jiang,1 and You Zhang11School of Mathematics and Statistics, ... equations,”Differential Equations and Dynamical Systems, vol. 2, no. 2, pp. 153–160, 1994.6 X. Lin, D. Jiang, and X. Li, “Existence and uniqueness of solutions forsingular k, n − k conjugateboundary ... Mαtn−1n − 2tn!−αh1, for t ∈ 0, 1.3.23Then, from 3.2, 3.21, 3.22 and 3.23,wehaveOn the other hand, for any x, y ∈ Qe,from3.13 and 3.14,wehavegTxt ≥ g1Mtn−1n...
... continuous and nondecreasing;h : 0, ∞ → 0, ∞ is continuous and nonincreasing, and h may be singular at y 0.Next, we consider the existence and uniqueness of solutions for the following singular higher-order ... ArticleExistence and Uniqueness of Solutions for Singular Higher Order Continuous and DiscreteBoundary Value ProblemsChengjun Yuan,1, 2Daqing Jiang,1 and You Zhang11School of Mathematics and Statistics, ... 1−αqj n − 1≤ Mei, for 0 ≤ i ≤ T 1.4.19On the other hand, for any x, y ∈ Qe,from4.10 and 4.12,wehavegxj ≥ g1Mej≥ eαj1Mαg1, for 1 ≤ j ≤ T, 4.20hyj...
... solutions of singularand nonsin-gular discrete problems via variational methods,” Nonlinear Analysis, vol. 58, no. 1, pp. 69–73,2004.[4] X. Cai and J. Yu, “Existence theorems for second- order ... Jour-nal of Mathematical Analysis and Applications, vol. 320, no. 2, pp. 649–661, 2006.[5] Z. Guo and J. Yu, “Existence of periodic and subharmonic solutions for second- order superlin-ear difference ... second, the third, and fourth variables and satisfies f (t + m,u,v, w)=f (t,u,v,w) for a given positive integer m.We may think of (1.1) as being a discrete analogue of the second- order functionaldifferential...
... matures. In thecase of forward foreign exchange contracts, the relationship is a bit more complex because itinvolves both foreign and domestic interest rates. The forward foreign exchange rate ... addition to providinginformation and matching buyers and sellers, dealers also provide immediacy by buying and selling from inventory. The bid-asked spread charged by dealers in secondary markets ... facilitate clearing and settlement of secondary market trading. Hong Kong, China, for example, has established acomputerized book-entry system for bonds to reduce clearing and settlement risk....
... cyclones; typhoons; and wind disasters. 1 Introduction In 1995, a design code TCVN 2737:1995 Loads and actions – norms for design [1] was issued for analysis and design of buildings and structures ... typhoons and nothing could compensate for human loss. This paper therefore provides the information on the typhoons in Vietnam as well as to introduce the technical solutions recommended for existing ... crops and the environment. In summary, typhoons and inundation are one of the many factors causing hunger and poverty hindering the socio-economic development of Vietnam. Therefore, planning and...
... always / like / see / my doctor/ once a year.7. I can't stand / get up / at five / tomorrow.8. The buses / usually / stop / run / before midnight.9. My father / seem / get / better / now.10....
... agreed upon, but/so we need to give it a second thought.Fifteen-minute test Grade: 12 basicFull name: Class: 12 Fill each blank with but, so, however or therefore where appropriate. 1. This is ... …………………. I was very sleepy.5. I washed my hands. …………………. , they still looked dirty.6. …………………. I washed my hands, they still looked dirty7. I washed my hands, …………………. they still looked dirty.8. ... be trustworthy10. Alan seems trustworthy and capable as a financial advisor, …………………. I wouldn't trust him with my money. Fifteen-minute test Grade: 12 basicFull name: Class: 12 Fill...
... is astudent and live in London. He gets up early and have braeakfast 7.00. He has a sport bike but he don’t go to work by bike. He go to work by bus. His classes starts at 7.15 and end at ... the kitchen and there is a living-room where there's a lovely old fireplace. there's a garden___________(5) the house. The garden_____(6) down to the beach and in spring and summer ... …(1)……….(be) a new student in class 7A. She……(2)…….(be) from Hue and her parents still ……(3)……(live) there. She …(4)………(live) with her uncle and aunt in Ha Noi.Hoa …(5)……(have) lots of friends in Hue....