problems with intervention studies for family caregivers

... approximation, 2.6 holds for any h ∈ W 1,∞ R with compact support and all 0} ξ ∈ {ξ ∈ L2 0, T ; V | ξt ∈ L2 Q , ξ ·, T Boundary Value Problems Now we can state the existence result for prolem P as follows ... existence of weak solution for problem Pn Since it is easy to prove the uniqueness of weak solution for problem Pn , we omit the details 6 Boundary Value Problems To deal with the time derivative ... of renormalized solution introduced by DiPerna and Lions in for Boltzmann equations see also 10–12 Boundary Value Problems As usual, for k > 0, Tk denotes the truncation function defined by ⎧ ⎪k,...

Ngày tải lên: 21/06/2014, 20:20

... cat kept interfer _g with my homework _ Final E Before Consonant Keep final silent e before a suffix beginning with a consonant amazement, atonement, hopeful, fortunately, useful Exceptions: ... Mechanical Drawing 2, Social Studies 3, Mathematics Do not capitalize the names of unnumbered courses except for languages: I’m taking mechanical drawing, social studies, mathematics, and German ... realize before dropped knew really believe embarrass knowledge receive benefit enough library recommend boundary every lightning resistance break exception maintenance rhythm continued PROBLEMS WITH...

Ngày tải lên: 23/10/2013, 13:20

... around here ⁄ PROBLEMS WITH MODIFIERS 191 Don’t say this here or that there to describe a noun This here cake was made without eggs Don’t use more with an -er word (more wiser) or most with an -est ... (have) written Forms of have and of be and are often used as helping verbs: has left, were chosen, agree PROBLEMS WITH VERBS 179 EXERCISE In each sentence, underline the correct form of the verb ... the present tense forms: First Person: Second Person: Third Person: PROBLEMS WITH VERBS I have we have you have you have he, she, it has they have 181 These are the past tense forms: I had we had...

Ngày tải lên: 23/10/2013, 13:20

... I) Mollie and me form a compound indirect OBJECT Go with Maura and him (not he) to the flea market Say: Go with Maura Go with him Go with Maura and him (not he) Maura and him form a compound OBJECT ... singular His her with or is singular Even though everybody “sounds” plural, it isn’t The use of their with everybody—or with any other word on the list—is incorrect in formal English With either ... the pronoun stands for. ) Look at the following sentence: iiiiiii x m A wolf is gentle with its young Its refers to wolf Wolf is the antecedent of its Wolf is singular Therefore, its is singular...

Ngày tải lên: 23/10/2013, 13:20

... sentence with a subordinate clause beginning with unless Unless Daria cleaned her room, she wasn’t allowed to have a television in it Write a simple sentence with a compound subject PROBLEMS WITH ... object, car, like a verb.) PROBLEMS WITH SENTENCE STRUCTURE 161 A gerund cannot make a complete sentence without a true verb NOT A SENTENCE: Winning the soccer match with a penalty kick SENTENCE: ... complete sentence without a true verb NOT A SENTENCE: To pick blackberries for a pie SENTENCE: Cara decided to pick blackberries for a pie SENTENCE: Cara picked blackberries for a pie EXERCISE...

Ngày tải lên: 23/10/2013, 13:20

... single-valued; (p8) E is a uniformly convex Banach space if and only if E* is uniformly smooth; (p9) If E is uniformly convex and uniformly smooth Banach space, then J is uniformly norm-to-norm continuous ... then, for all x, y Î E, j(x; y) = if and only if x = y; (2) If E is a Hilbert space, then j(x, y) = ║x - y║2 for all x; y Î E; (3) For all x, y Î E, (║x║ - ║y║)2 ≤ j(x, y) ≤ (║x║ + ║y║)2 For solving ... doi:10.1016/j.na.2008.02.042 Yao, Y, Cho, YJ, Chen, R: An iterative algorithm for solving fixed point problems, variational inequality problems and mixed equilibrium problems Nonlinear Anal (TMA) 71, 3363–3373 (2009) doi:10.1016/j.na.2009.01.236...

Ngày tải lên: 20/06/2014, 21:20

... solutions for boundary value problems with integral boundary conditions on time scales Motivated by the statements above, in this paper, we are concerned with the following boundary value problem with ... value problems with integral boundary conditions on time scales also cover two-point, three-point, , n-point boundary problems as the nonlocal boundary value problems in the continuous case For ... of 18 problems with integral boundary conditions constitute a very interesting and important class of problems They include two-point, three-point, multipoint and nonlocal boundary value problems...

Ngày tải lên: 20/06/2014, 22:20

... regularity theory for very weak solutions of the A-harmonic equations with w(x) ≡ have been considered [4], and the regularity theory for very solutions of obstacle problems with w(x) ≡ have been ... This paper gives a Caccioppoli-type estimate for solutions to obstacle problems with weight, which is closely related to the local regularity theory for very weak solutions of the A-harmonic equation ... we understand any domain of finite measure for which the estimates for the Hodge decomposition in (2.1) and (2.2) are satisfied A Lipschitz domain, for example, is regular We consider the second-order...

Ngày tải lên: 20/06/2014, 22:20

... c∞ and if c := c j = = c j+l for ≤ j ≤ j + l ≤ dim H- with l ≥ 1, then i(Kc ∩ S) ≥ l + ≥ Therefore, J has at least dim H- -1 pairs of sign-changing critical points with values belong to [c0, c∞] ... theory with applications to differential equations CBMS Reg Cof Ser Math 65 (1986) doi:10.1186/1687-2770-2011-18 Cite this article as: Qian: Sign-changing solutions for some nonlinear problems with ... {uk} ⊂ J-1 (]c1, c2[), for which {J(uk)} is bounded and J’(uk) ® 0, possesses a convergent subsequence, and Qian Boundary Value Problems 2011, 2011:18 http://www.boundaryvalueproblems.com/content/2011/1/18...

Ngày tải lên: 21/06/2014, 00:20

... following conditions: f0 for each x ∈ K, F x, x 0; f1 for each x, y ∈ K, F x, y ∩ − int P ∅ implies that F y, x ⊂ −P ; f2 for each x ∈ K, F x, · is P -convex on K; f3 for each x ∈ K, F x, · is ... fulfilled Indeed, for each x, y ∈ K and for any sequence {ξn } ⊂ {ξ ∈ x, y : − int P ∅ By F ξ, y − int P ∅} with ξn → ξ0 , we have ξ0 ∈ x, y and F ξ0 , y the lower semicontinuity of F ·, y , for any z ... does not hold, then there exists a sequence {xn } ⊂ K such that for each n, xn ≥ n and F y, xn ⊂ −P for every y ∈ K with y ≤ n Without loss of generality, we may assume that dn xn / xn weakly...

Ngày tải lên: 21/06/2014, 06:20

... assumptions: A1 αi > for i m−2 i 1, , m − 2, with < αi < 1; A2 f ∈ C R \ {0}, R ∩ C R, R satisfies f s s > for s / 0; ∞; A3 f0 : lim|s| → f s /s A4 f∞ : lim|s| → ∞ f s /s ∈ 0, ∞ Let Y C 0, with the norm ... 1/k for some j ∈ {0, 1, , k − 1} Then, for this j j j j j Il j, τl − τl > 3/4k if l is large enough Put τl , τl j Obviously, for the above given k, ν and j, yl t have the same sign on Il for ... , for any σ > small enough, yl t ≥ σ yl j Il ,∞ , j ∀t ∈ τl j σ, τl −σ 3.32 j This together with 3.31 implies that there exist constants α, β with α, β ⊂ I∞ , such that ∞, lim yl t l→∞ uniformly...

Ngày tải lên: 21/06/2014, 11:20

... for the three problems does not Conclusions Green’s function for problems with additional conditions is related with Green’s function of a similar problem, and this relation is expressed by formulae ... quadrature formula for the integral A x u x dx approximation n e.g., trapezoidal formula A, u trap : k Ak uk hk 1/2 Boundary Value Problems 21 The expression of Green’s function for the problem with ... Value Problems 17 Formulaes 5.25 and 5.26 easily allow us to find Green’s function for an equation with two additional conditions if we know Green’s function for the same equation, but with other...

Ngày tải lên: 21/06/2014, 11:20

... solutions for more general multi-point boundary value problems x (t) = g(t, x(t), x (t)) + e(t), m−2 x(0) = a e t ∈ (0, 1) m−2 hi x(τi ), x (1) = i=1 ki x (ξi ) i=1 For further background information ... x3 ) for (t, x1 , x2 , x3 ) ∈ (0, 1) × R × R × R (H3 ) f (t, x1 , x2 , x3 ) lim (|x1 |+|x2 |+|x3 |)→+∞ |x1 |+|x2 |+|x3 | = +∞ for t uniformly on [0, 1] Remark 2.1 From (H2 ) we know that for given ... satisfies the problem (1.1) The existence of positive solutions for multi-point boundary value problems has been widely studied in recent years For details, see [1–15] and references therein We note that...

Ngày tải lên: 21/06/2014, 17:20

... the existence of positive solutions for higher order p-Laplacian m-point boundary value problems with nonlinearity f being nonnegative on time scales Therefore, it is a natural problem to consider ... fΔ t σ t − s ≤ |σ t − s| 2.2 for all s ∈ U For f : T → R and t ∈ Tk , the nabla derivative of f at t, denoted by f ∇ t provided it exists with the property that for each > 0, there is a neighborhood ... dynamic equations with sign changing nonlinearity,” Acta Mathematica Scientia, vol 52, pp 181–196, 2009 Chinese 14 F Y Xu, “Positive solutions for multipoint boundary value problems with one-dimensional...

Ngày tải lên: 21/06/2014, 20:20

... Value Problems Then the eigenvalues are mπ τm for m 1, 2, , 2.2 and the corresponding eigenfunctions are φm t sin mπt for m 1, 2, 2.3 Let G t, s be the Green’s function for the BVP: for t ... t ≤1 ω1 t ≤ ψ s, ds for t ∈ 0, , n ∈ N 2.14 If we let ω t limn → ∞ ωn t for t ∈ 0, , then ω ∈ C 0, , −ω t ω t > for t ∈ 0, , ψ t, ω t ω ω for t ∈ 0, , 2.15 Boundary Value Problems Next we consider ... 0, , ωn t > 0, ω t > for t ∈ 0, such that −ωn t g2 t, n ωn ωn t ≤ ωn t ≤1 ω t −ω t for t ∈ 0, , ωn ωn 0, for t ∈ 0, , n ∈ N, ω1 t ≤ a1 n→∞ for t ∈ 0, , g2 t, ω t ω 2.23 for t ∈ 0, , lim ωn t...

Ngày tải lên: 21/06/2014, 20:20

... and Applications Vector equilibrium problems, which contain vector optimization problems, vector variational inequality problems, and vector complementarity problems as special case, have been ... KuhnTucker condition for VEPC is both necessary and sufficient under the condition of cone-preinvexity Meanwhile, we obtain the optimality conditions for vector optimization problems with constraints ... → X such that for any x, y ∈ S, and t ∈ 0, , x tη y, x ∈ S Let S ⊂ X be a invex set with respect to η A mapping f : S → Y is said to be C-preinvex with respect to η see 19 , if for any x, y ∈...

Ngày tải lên: 22/06/2014, 02:20

... equilibrium problems We introduce several types of Levitin-Polyak well-posedness for equilibrium problems with abstract and functional constraints Necessary and sufficient conditions for these types ... problems with both abstract and functional constraints 33, 34 Very recently, Huang and Yang 35 studied Levitin-Polyak-type wellposedness for generalized variational inequality problems with abstract ... for convex scalar optimization problems with functional constraints started by Konsulova and Revalski 32 Recently, Huang and Yang generalized those results to nonconvex vector optimization problems...

Ngày tải lên: 22/06/2014, 06:20

... results for second order nonlinear problems with maximum and minimum,” e Mathematische Nachrichten, vol 192, no 1, pp 225–237, 1998 S Stanˇ k, “Multiplicity results for functional boundary value problems, ” ... same time, for k ∈ {α, , β − 1}, we have Δu k > and β Δu k Δu β − Δ2 u i − , Δu k Δ2 u i − 2.31 i α i k For k k Δu α β, we get β ≥ Δu β β Δu α Δ2 u i − ≥ i α Δ2 u i − 2.32 i α So, for k ∈ {α, ... k∈{α, ,ξ1 −1} Δu k , k ∈ α, , ξ1 2.48 For k ∈ {α, , β − 1}, we have β Δu k Δu β − Δ2 u i − i k 2.49 R Ma and C Gao Together with Δu β ≤ and Δu k > 0, for k ∈ {α, , β − 1}, we get β Δu k...

Ngày tải lên: 22/06/2014, 11:20

... iteration scheme with perturbed mapping for approximation of common fixed points of a finite family of nonexpansive selfmappings of H We will establish strong convergence theorem for this explicit ... for variational inequalities,” to appear in Taiwanese Journal of Mathematics [13] L.-C Zeng and J.-C Yao, “Implicit iteration scheme with perturbed mapping for common fixed points of a finite family ... x∗ (2.18) i→∞ n→∞ Without loss of generality, we may further assume that xni → z weakly for some z ∈ H By Lemma 1.8 and (2.16), we have z ∈ Fix Wn , (2.19) this together with Proposition 1.5...

Ngày tải lên: 22/06/2014, 19:20

... systems,” Boundary Value Problems, vol 2005, no 2, pp 93–106, 2005 [23] Z Drici, F A McRae, and J Vasundhara Devi, “Monotone iterative technique for periodic boundary value problems with causal operators,” ... ,θ1 ] for n = 0,1,2, Since Ω is compact by Lemma 2.4, therefore, we assert that the sequence {αn }∞ has a n= convergent subsequence {αnk }∞ such that αnk → α∗ k= Since α1 ∈ P[θ2 ,θ1 ], therefore, ... solutions for the one-dimensional p−Laplacian boundary value problems, ” Nonlinear Analysis, vol 56, no 7, pp 975–984, 2004 [14] J Li and J Shen, “Existence of three positive solutions for boundary...

Ngày tải lên: 22/06/2014, 19:20