solving systems of nonlinear equations in three variables

... constantly increasing interest in developing the theory and numerical approaches for HPD (Hermitian positive definite) solutions to different classes of nonlinear matrix equations (see [8-21]) In this ... Ivanov, I, Minchev, B, Hasanov, V: Positive definite solutions of the equation X − A∗ X−1 A = I In: Heron Press S (ed.) Application of Mathematics in Engineering’24, Proceedings of the XXIV Summer ... systems of nonlinear matrix equations involving Lipshitzian mappings Fixed Point Theory and Applications 2011 2011:89 Submit your manuscript to a journal and benefit from: Convenient online submission...

Ngày tải lên: 20/06/2014, 22:20

... linear equations, J Number Theory 102 (2003), 11-22 [10] I.Z Ruzsa, Solving a linear equation in a set of integers I, Acta Arith 65 (1993), 259-282 [11] I.Z Ruzsa, Solving a linear equation in ... proof of Lemma 2.1 Lemma 2.2 Let A be an L-avoiding subset of [1, n] of maximum size Let s = sA and t := max{i ∈ N : ri ≥ s} If n b,c then t = Proof : Just follow the reasoning in the proof of ... crucial point is that, since n < c, the intervals I1 and I2 are disjoint Each interval certainly contains at least three elements by (12) It is then easy to see that the I2 -pairing will certainly...

Ngày tải lên: 07/08/2014, 15:23

... inequality (2.3) implies The following definition, which is a modified version of one introduced in [3], provides a kind of the strict inequality in X Definition 2.5 Let H be a linear manifold in ... = in the topology of X Since (2.21) can be rewritten in the form of the inclusion βm f − x, βm f + x ⊂ K, (2.22) taking into account the closedness of K and passing to the limit as m → +∞ in ... (2.29) is nonlinear Mutual comparability of solutions of (1.1) The aim of this section is to establish certain conditions under which each two solutions of (1.1) lying in a certain linear manifold...

Ngày tải lên: 22/06/2014, 18:20

... (continuous) Schlesinger transformation in this case equals R(ζ) = (ζ − xi )±1 Proof of Theorem 5.3 Arguing as in the proof of Lemma 5.2, we can show that all the statements used in this proof ... differential analog of the periodic matrix P , which contains all integrals of motion in the case of difference equations, gives only the monodromy information at in nity and does not carry any information ... analytically continue any solution Y(ζ) of (5.1) or (5.2) along a closed path γ in C avoiding the singular points {xk } then the columns of Y will change into their linear combinations: Y → YMγ...

Ngày tải lên: 14/02/2014, 17:20

... properties of linear Volterra integro-differential equations, ” Mathematical Models & Methods in Applied Sciences, vol 18, no 1, pp 21–45, 2008 L Pandolfi, “Riesz systems and controllability of heat equations ... Mathematics, Springer, Berlin, Germany, 1998 12 Advances in Difference Equations T Xiao and J Liang, “Laplace transforms and integrated, regularized semigroups in locally convex spaces,” Journal of Functional ... iλ α β −1 ∈σ A 2.15 is countable Proof As in 9, Section , we take M: e−βs x : x ∈ X ⊂ Lp R , X 2.16 In view of the discussion in 8, Lemma VI.7.23 , we can infer that C ⊂ ρ A|D , λ λ β ∈ρ A ,...

Ngày tải lên: 21/06/2014, 05:20

... continuity of q in the semispace z > 6 Advances in Difference Equations Case β2 Recall that, since we are assuming that inequality 2.6 holds, we have β1 α2 / In this case, the forbidden set of ... be to give a description of the dynamics of the system in terms of the eigenvalues of the associated matrix A given in 2.2 We begin with the following result concerning 2-periodic solutions ... stability of fixed points in some of the cases Recall that a fixed point of our system x∗ , y∗ always verifies y∗ λ for some real eigenvalue λ of the matrix A We will say in such case that the fixed point...

Ngày tải lên: 21/06/2014, 05:20

... Advances in Difference Equations It is obvious that under these two conditions, ϕ is an homeomorphism from R onto R and is increasing on R Recall that p-Laplacian equations have been of great interest ... 0,T ∞ 1.4 max{|x|∞ , |x |∞ }, where max x t 1.5 t∈ 0,T In the proof of our main results, we will need the following classical Mawhin’s continuation theorem Lemma 1.1 Let (H1), (H2) hold and f ... solution of 2.2 By integrating the two sides of 2.2 x T and x x T , we have over 0, T , and noticing that x T g x t − e t dt 0, 2.3 e t dt 2.4 that is, T Since g x · T g x t dt e: T T is continuous,...

Ngày tải lên: 21/06/2014, 18:20

... recently, by using Shauder fixed point theorem, Guo 15 obtained the existence of positive solutions for a class of nth-order nonlinear impulsive singular integro-differential equations in a Banach ... Equations in Banach Spaces, vol 596 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 1977 V Lakshmikantham and S Leela, Nonlinear Differential Equations in Abstract Spaces, vol of International ... Liu, Nonlinear Integral Equations in Abstract Spaces, vol 373 of Mathematics and Its Applications, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1996 K Deimling, Ordinary Differential Equations...

Ngày tải lên: 21/06/2014, 20:20

... quasilinear systems, ” The Rocky Mountain Journal of Mathematics, vol 37, no 1, pp 215–228, 2007 [22] R Ma, “Multiple nonnegative solutions of second-order systems of boundary value problems,” Nonlinear ... number of positive solutions of nonlinear systems, ” Journal of Mathematical Analysis and Applications, vol 281, no 1, pp 287–306, 2003 [24] Y Zhou and Y Xu, “Positive solutions of three- point boundary ... Society, vol 46, no 1, pp 75–86, 2003 [19] G Infante and J R L Webb, “Loss of positivity in a nonlinear scalar heat equation,” Nonlinear Differential Equations and Applications, vol 13, no 2, pp...

Ngày tải lên: 22/06/2014, 00:20

... we obtain the existence of a mapping c : G → Y such that the following hold i c is a fixed point of J, that is, c x F x, c η x ∀x ∈ G , 4.13 The mapping c is the unique fixed point of J in the ... suggestions in improving this paper References D H Hyers, “On the stability of the linear functional equation,” Proceedings of the National Academy of Sciences of the United States of America, ... approximation of approximately linear mappings by linear mappings,” Journal of Functional Analysis, vol 46, no 1, pp 126–130, 1982 J M Rassias, “Solution of a problem of Ulam,” Journal of Approximation...

Ngày tải lên: 22/06/2014, 06:20

... quasilinear systems, ” The Rocky Mountain Journal of Mathematics, vol 37, no 1, pp 215–228, 2007 [22] R Ma, “Multiple nonnegative solutions of second-order systems of boundary value problems,” Nonlinear ... number of positive solutions of nonlinear systems, ” Journal of Mathematical Analysis and Applications, vol 281, no 1, pp 287–306, 2003 [24] Y Zhou and Y Xu, “Positive solutions of three- point boundary ... Society, vol 46, no 1, pp 75–86, 2003 [19] G Infante and J R L Webb, “Loss of positivity in a nonlinear scalar heat equation,” Nonlinear Differential Equations and Applications, vol 13, no 2, pp...

Ngày tải lên: 22/06/2014, 06:20

... of two nonlinear difference equations, ” Communications on Applied Nonlinear Analysis, vol 5, no 2, pp 47–59, 1998 10 G Papaschinopoulos and C J Schinas, “Invariants for systems of two nonlinear ... difference equations, ” Advances in Difference Equations, vol 2007, Article ID 31272, 13 pages, 2007 12 B Iri´ anin and S Stevi´ , “Some systems of nonlinear difference equations of higher order with c c ... suggestions that improved the quality of this study References G Papaschinopoulos and C J Schinas, “On a system of two nonlinear difference equations, ” Journal of Mathematical Analysis and Applications,...

Ngày tải lên: 22/06/2014, 11:20

... invertible p Proof We first note that the following proof is inspired by the proof of [14, Theorem 4.5] (i)⇒(ii) Let Pn , n ∈ N, be a family of projections given by the exponential dichotomy of ... exponential dichotomy of (1.1) using invertibility of a certain operator derived from the operator T In order to obtain such a characterization, we have to know the subspace kerP0 in advance (see Theorem ... solvability of (1.2) in l∞ spaces of sequences defined on N In the present paper, we will characterize the exponential dichotomy of (1.1) by the solvability of (1.2) in l p spaces (1 ≤ p < ∞) of sequences...

Ngày tải lên: 22/06/2014, 22:20

... as in the proof of Lemma 3.5 Combining this with the weak Harnack inequality above one obtains the full Harnack inequality with the constant depending on the Lq s (B4R )norm of the solution instead ... lder continuity,” Nonlinear Analysis, o vol 36, no 3, pp 295–318, 1999 [9] Yu A Alkhutov and O V Krasheninnikova, “Continuity at boundary points of solutions of quasilinear elliptic equations ... semicontinuous since u∗ (x) = essinf y∈B(x,r) u(y) is lower r semicontinuous and u∗ is an increasing limit of the functions u∗ r We will complete the proof for bounded functions u by showing that...

Ngày tải lên: 22/06/2014, 22:20

... Tsuji, Formation of singularities for Monge-Amp`re equations, Bull Sci e Math (1995) 433–457 M Tsuji and H T Ngoan, Integration of hyperbolic Monge-Amp`re equations, e In: Proceedings of the Fifth ... = and (3.9) = Continuation of the proof of Theorem 2.8 for n = Since dim X1 = 3, we can choose , , as a basis of X1 Similarly, since dimX2 = 2, we can chose , as a basis of X2 We prove that ... needed, in the case n we get only particular results The outline of the paper is the following In Sec we recall the notions of weak hyperbolicity and hyperbolicity for (1.1) In the following Secs...

Ngày tải lên: 06/08/2014, 05:20

... oak (Q velutina) We summarize herein the results of a prior study that examined internal and external factors which influence the size of acorn crops in these species (Sork et al, in press) and ... illustrate the biology of flowering and fruiting in oaks Ecologists often call the phenomenon producing good crops some years and poor crops in other years, mast-seeding or mast-fruiting (Janzen, 1971; ... Development of Trees vol II Academic Press, New York Minima EG (1954) Biological basis of flowering and fruit bearing in oak Tr Inst Lesa Akad Nauk SSSR 17, 5-97 (translated and published by Indian...

Ngày tải lên: 08/08/2014, 19:21

... positions in their re-sequencing of CEPH families The interesting feature of this region is the fact that it harbors insertion/deletion variation [24-27], and therefore we were interested in examining ... lists of indices corresponding to positions in the sequence string allowing the program to account for circularity by creating some discontinuous lists (spanning the origin) Next, sublists within ... without interruption At site 7,028 the heteroplasmy shift is of somatic origin (it occurred in blood of M4C3), while at site 8992 it is of germline origin (both analyzed tissues of M4C1 have increased...

Ngày tải lên: 09/08/2014, 23:20

... http://ccforum.com/content/15/3/424 Page of Figure CT images of lung and maxillofacial bones, inspired tooth in case (a-d) CT scan on day showed the tooth-like foreign body (white/black arrow) in the right bronchus ... fracture of mandible and left zygomatic arch, and loss of three teeth (f,g) Obstructive pneumonia developed in the right lower lobe on day (h) Flexible bronchoscopy confirmed the tooth in the right ... bronchus (i) The central incisor removed by flexible bronchoscopy on day (j-l) Chest CT (day 13) and radiography (day 24) showed extinction of obstructive pneumonia in the right lower lobe doi:10.1186/cc10148...

Ngày tải lên: 14/08/2014, 08:21

... across the three discipline; • the sequencing of moves within the introductions and the conclusions across the three disciplines; and, • the linguistic realization of each move in the introductions ... Realizations in Zoology Introductions 7.6 Discussion of Findings …………………………………………… 7.6.1 Move in the Introductions ………………………………… 7.6.2 Move in the Introductions ………………………………… 7.6.3 Move in the Introductions ... the three disciplinary communities investigated in this study These findings have important implications for studies in disciplinary discourse, writing pedagogy and future research in disciplinary...

Ngày tải lên: 12/09/2015, 21:26

... the University administration and around the city of Singapore Many people helped me in Indonesia by talking to me, giving me advice, inviting me into their homes and watching the World Cup with ... Buehler, “The Rising Importance of Personal Networks in Indonesian Local Politics: An Analysis of District Government Head Elections in South Sulawesi in 2005,” in Deepening Democracy in Indonesia? ... enjoy influence over and access to provincial and central state institutions Machines will be most influential in provinces where one party dominates the provincial government By combining party...

Ngày tải lên: 13/10/2015, 15:57