... banks themselves Because lending activity has created a major source of income to meet expenses such as, return on deposits and customer loans, offset business costs and generate profits for ... process of making loans which focuses on creating favorable conditions for customers and ensures the safety of loans There always exists the companion of the bank in customers’ process of using ... The result gained from the analysis is used to assess the efficiency of THQV s consumer loans and find out the strength, the weakness as well as the reason for its shortcomings Then, based on...
... is applied at surfaces of the coastal structures. Zero gradients of k and ε are assumed at the offshore, lateral boundaries and at surfaces of coastal structures. A scheme ... Vu Thanh Ca / VNU Journal of Science, Earth Sciences 23 (2007) 159‐168 figure suggests that the model can simulate nearshore wave processes, such as wave energy loss due to breaking, wave setup, setdown etc. with acceptable accuracy. ... status of a beach depends on the cross‐shore transport of sediment, which is closely related with wave conditions. If the shoreward transport of sediment by incoming waves ...
... Flexible Savings This strategic product was specifically designed for individual customers This Service offers customers highest autonomy and best interest rate This Service also allows customers to ... line with the changes of market interest rates This shows the flexibility and responsiveness of VPBank s business Currently VPBank applies rates for deposits, savings deposits normally are: Nguyen ... firstly should define the core needs of its customers, create the specific image of the products and services to stimulate customers’ demand This is also the basis for customer to distinguish...
... discuss the existence of periodic solutionsfor the higherorder difference equation x(n + k) = g(x(n)) − f (n, x(n − τ (n)) We show the existence of periodic solutionsby using Schauder s fixed point ... main results of this article are following sufficient conditions which guarantee the existence of a periodic solution for (1.1) Theorem 1.1 Assume that there exist constants m < M, r > such that ... positive constants, τ : Z → Z and τ (n + ω) = τ (n), ω, m, k ∈ N, and obtained existence theorem for single and multiple positive periodic solutionsof (1.3) Our aim of this article is to study...
... are sign changing and Ω is bounded, [18] studied (1.1) and obtained that there exists Λ >0 such that (1.1) has at least two positive solutionsfor all l Î (0, Λ) For the case p ≠ 2, [19] studied ... assumptions < q < p < N, N > p , −∞ < μ < μ and f, g are nonnegative They also proved that there existence of Λ0 >0 ¯ such that for l Î (0, Λ0), (1.1) possesses at least two positive solutions ... (N ≥ 3) By extracting the Palais-Smale sequence in the Nehari manifold, the existence of at least two positive solutionsof (1.1) is verified The following assumptions are used in this paper:...
... organized as follows In Section 2, we present some assumptions and definitions needed for this study Section is devoted to the proof of the uniform decay result In Section 4, we prove the blow-up result ... and b = and for a wider class ofrelaxation functions He established a more general decay result, for which the usual exponential and polynomial decay results are just special cases For the finite ... blow-up result forsolutions with negative initial energy if p >m ≥ and a global result for ≤ p ≤ m This result has been later improved by Messaoudi [12] to accommodate certain solutions with positive...
... u s vt t x s x s t t y x rfYhv YtbsDiwt&wX&bqsbq0AtârfYhv YtbsD9&bvrx&P&sebdrbs2ibxhHvYbsS q8 l b&byxwptbsTwy o ss x xt Ysnbqmhb0edYs l wy YbsTbvxbcxHvjAqihVfxhe&YyhHHYsbyh&8Hhbq9&r0bqPbsbsTrwbqhwuhrApi ... y g x s y v y sot d s tq s g sq y x o xy yo u !i&ashbq2 Ydhbqx &mHshuh8jueqmri&t bsiYbsTbvxbvHcx wHwtYihbqsHYvHhnwSTms u vysxwvtsFrq y t q g d xt y y x s d x sss t s g xt ... Ơ Ơ Ơ âĐ Ơ Đ Ô Â uy y s gy s x ss x x v s g ot x fq y d y so s k d q p hrgx &na0!n&Ybssx mhbqbyâhbyYs bqxi2&bysbcxYHTicx8egwmbsHYhmhbqx hhv sv r " i V05 (&( v0 &$0...
... papers 1–3, 11–14 , the authors studied the existence of periodic solutions, subharmonic solutions, and homoclinic solutionsof some special forms of 1.1 by using the critical point theory These ... Advances in Difference Equations Equation 3.18 shows that u ρ implies that I u ≥ α, that is, I satisfies assumption ii of Lemma 2.1 Finally, it remains to show that I satisfies assumption iii of Lemma ... proofs of assumption ii of Lemma 2.1 Therefore, we only proves assumption ii of Lemma 2.1 still hold that using F1’ instead of F1 By F1’ , there exists η ∈ 0, such that f n, x ≤ q n |x|δ for...
... respectively The existence of ground state solutionsof Eb is affected by the shape of the domain Ω and b x that satisfies some suitable conditions and has been the focus of a great deal of research ... 3.9 for some positive constant d0 This completes the proof We define the Palais-Smale simply by P S conditions in H0 Ω for Jλa,b as follows sequences, P S -values, and P S - Definition 3.2 (i) For ... for all x Dirichlet problem −Δ in Ω It was obtained there existence of Λ0 > such that for λ ∈ 0, Λ0 , Eλa,b possesses at least two positive solutions In a recent work 19 , Hsu and Lin have studied...
... Problems h t ≡ 0, Korman investigated the uniqueness of positive solutionsof the problem 1.1 by techniques of bifurcation theory However, the existence of sign-changing solution for this problem ... Finally in Section 3, we state and prove our main result Remark 1.1 For other results on the existence and multiplicity of positive solutions and nodal solutionsfor boundary value problems of ordinary ... 3, pp 389–392, 2004 Chinese P Korman, “Uniqueness and exact multiplicity ofsolutionsfor a class of fourth-order semilinear problems,” Proceedings of the Royal Society of Edinburgh A, vol 134,...
... of the existence ofsolutions are imposed such as periodicity, asymptotic stability and oscillatory [10–12] In [13], the authors discusses the existence of univalent solutionsfor fractional integral ... equations with maxima in complex domain, by using technique associated with measures of non-compactness In this article, we establish the extreme solutions (maximal and minimal solutions) for fractional ... control of various technical systems It often occurs that the law of regulation depends on maximum values of some regulated state parameters over certain time intervals Many studies of the existence...
... properties of spaces W 1,p(x) (Ω) which will be used later (for details, see [17]) Denote by S( Ω) the set of all measurable real functions defined on Ω Two functions in S( Ω) are considered as the same ... X-topology Proof of theorems In this section we shall prove Theorems 1.1–1.3 Since only the positive solutions are considered, without loss of generality, we can assume that f (x, t) = f (x, 0) for t ... This shows that w1 is a supersolution of the problem Pλ1 Obviously is a subsolution of f f Pλ1 By Theorem 3.3, Pλ1 has a solution uλ1 such that ≤ uλ1 ≤ w1 By Proposition 18 3.4, uλ1 > on Ω So...
... x s ds x s ds t0 t−T t ≤ 2x t0 2.7 t0 x s ds t0 x s ds t−T T ≤ 2e x s ds, which gives that |x|∞ ≤ e |x|∞ ≤ |e| T x s ds 2.8 x s ds 2.9 Thus, Since lims → ∞α s T ∞, there is a constant M > such ... t 1.3 e t, |s| p−2 sfors / and ϕp 0 Obviously, 1.3 is a special case and its variants, where ϕp sof 1.1 However, there are seldom results about the existence of periodic solutions to 1.1 The ... existence of periodic solutions to 1.1 Therefore, in this paper, we will devote ourselves to investigate the existence of periodic solutions to 1.1 As one will see, our theorem generalizes some...
... ≤ cα1 −β1 n ,y s n s, x s Hn σn t , s f t α1 n ds n ds ds α2 1− y s n α2 f s, 1, ds f s, 1, ds − s f s, 1, ds n s − s f s, 1, ds 1/n ≤ μn cα1 −β1 α2 −β2 −α1 −α2 n s − s f s, 1, ds aμn cα1 −β1 ... xm s 1/n ≤ xm , ym − 1−1/n Hn σn t , s f , ym s n s, xm s 1/n ≤ μn 1−1/n s 1/n n 1− s n f n s, xm s n −f −f , ym s n ,y s n s, x s ,y s n s, x s −f n s, x s n n ,y s n ds ds n ds 2.30 Consequently, ... Value Problems The study of system of BVPs has also fascinated many authors System of BVPs with continuous nonlinearity can be seen in 20–22 and the case of singular nonlinearity can be seen in 8,...
... not necessarily hold So it is interesting and important to discuss the problem 1.1 The purpose of this paper is to prove that the problem 1.1 possesses at least two positive solutions Moreover, ... Birkh¨ user, Boston, Mass, USA, 2001 a 12 M Bohner and A Peterson, Eds., Advances in Dynamic Equations on Time Scales, Birkh¨ user, Boston, a Mass, USA, 2003 13 D R Anderson, “Extension of a second-order ... has at least one fixed point in P ∩ Ω2 \ Ω1 Main Results In this section, we apply Lemma 2.6 to establish the existence of at least two positive solutionsfor BVP 1.1 The following assumptions...
... As the function ϕ x t∈ 0,1 G t, s f s, u s − f s, v s ds 3.6 G t, sss f s, u s max t∈ 0,1 −σ σ max − f s, v s ds G t, s s−σ λ · ln u s − v s ds ln x is nondecreasing then, for u ≥ v, ln u s ... operator T is nondecreasing since, by hypothesis, for u ≥ v G t, s f s, u s ds Tu t G t, s s−σ s f s, u s ds 3.5 ≥ G t, s s−σ s f s, v s ds Tv t Besides, for u ≥ v d T u, T v max | T u t − T v t ... if we suppose that u t2 − u t1 then G t2 , s − G t1 , s f s, u s ds a.e as, G t2 , s − G t1 , s > we deduce that f s, u s On the other hand, if f s, u s a.e then G t, s f s, u s ds u t for t...
... basic results on the existence ofsolutionsof the system; these results correspond to the sublinear and superlinear cases for p 2, respectively Inspired by the above-mentioned papers, we concern ... Antontsev and S Shmarev, “Elliptic equations and systems with nonstandard growth conditions: existence, uniqueness and localization properties of solutions, ” Nonlinear Analysis: Theory, Methods & Applications, ... points of J u, υ are the weak solutionsof the system P,Q Theorem 3.5 The system P,Q has at least one nontrivial solution u, υ Proof By Lemmas 3.3 and 3.4, we can apply the mountain pass theorem...
... conditions see 17–20 On the existence ofsolutionsfor p x Laplacian systems boundary value problems, we refer to 5, 7, 10, 11 But results on the existence ofsolutionsfor weighted p t -Laplacian systems ... discuss the existence ofsolutionsof 1.1 - 1.2 in the following two cases: i f satisfies sub-p− − growth condition; ii f satisfies general growth condition This paper is divided into four sections ... This completes the proof f satisfies sub-p− − growth condition In this section, we will apply Leray-Schauder s degree to deal with the existence ofsolutionsfor 1.1 - 1.2 , when f satisfies sub-p−...
... multiple solutionsof elliptic systems,” Transactions of the American Mathematical Society, vol 355, no 7, pp 2973–2989, 2003 P L Felmer, “Periodic solutionsof “superquadratic” Hamiltonian systems,” ... } is bounded in E As E is reflexive, passing to a subsequence, still denoted by {zn }, we may assume that there Journal of Inequalities and Applications 1,p x exists z ∈ E such that zn → z weakly ... open covering of Ω As Ω is compact, we can pick a finite subcovering n {Q x }n for Ω Thus there exists a sequence of open set {Ωi }n such that Ω i i i Ωi and pi sup p x < μi− inf μ x , for i 3.23...