... real Banach space and L : E → E be ** a ** compact linear map If there exists μ ∈ R 0, ∞ and / v ∈ E such that v μLv, μ is said to be ** a ** real characteristic ** Boundary ** ** Value ** Problems ** value ** ** of ** L The set ** of ** ... diﬀerential equations,” Applied Mathematics and Computation, vol 89, no 1-3, pp 133–146, 1998 R Ma and N Castaneda, “Existence ** of ** solutions ** of ** nonlinear ** m-point ** ** boundary-** ** value ** problems,” Journal ** of ** Mathematical ... 2 ** Boundary ** ** Value ** Problems Multi-point ** boundary ** ** value ** problems ** for ** ordinary diﬀerential equations arise in diﬀerent areas ** of ** applied mathematics and physics The existence ** of ** solutions ** of ** the...

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... ** Digivance® ** SCS ** 800/900 ** ** **** ESMR,1** 900 ** MHz ** ** and ** ** 800/900 ** ** ESMR, ** ** 1900 ** ** MHz ** ** Tri-Band ** ** Systems ** 12/06 • 103277AE ** Digivance® ** ** Street-Level ** ** Coverage ** ** Solution ** Overview With increased popularity ** and ** reliance ... Unit ** 1900 ** ** MHz ** Dual-band enclosure with two frequency bands +1-952-938-8080 • 1-800-366-3891 ** Digivance® ** Digivance® ** Street-Level ** ** Coverage ** ** Solution ** SCS ** 800/900 ** ** **** ESMR,1** 900 ** MHz ** ** and ** ** 800/900 ** ** ESMR, ** ** 1900 ** ** MHz ** ... typical ** and ** subject to change www.adc.com • +1-952-938-8080 • 1-800-366-3891 ** Digivance® ** Digivance® ** Street-Level ** ** Coverage ** ** Solution ** SCS ** 800/900 ** ** **** ESMR,1** 900 ** MHz ** ** and ** ** 800/900 ** ** ESMR, ** ** 1900 ** ** MHz ** ** Tri-Band ** Systems...

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... jumping problems ** with ** ** Dirichlet ** ** boundary ** condition In this paper we improve the multiplicity results of the single ** fourth ** ** order ** ** elliptic ** problem to that of the ** fourth ** ** order ** ** elliptic ** ** system ** Our main ... a semilinear ** elliptic ** problem Diff Integ Equat 5(3), 561–565 (1992) doi:10.1186/1029-242X-2011-60 Cite this article as: Jung and Choi: ** Fourth ** ** order ** ** elliptic ** ** system ** ** with ** ** dirichlet ** ** boundary ** condition ... Lemma 2.1, the solution u Î H We complete the proof ■ Abbreviations (FESDBC): ** fourth-** ** order ** ** elliptic ** ** system ** ** with ** ** Dirichlet ** ** boundary ** condition Acknowledgements This work(Tacksun Jung) was supported...

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... Diﬀerentialgleichung y Society of Japan, vol 1937, no 3, pp 861–866, 19 15 ** A ** Cabada, “An overview of the lower and upper solutions method ** with ** nonlinear ** boundary ** ** value ** conditions,” ** Boundary ** ** Value ** Problems, ... Gyulov, and ** A ** I Santos, “Existence and location result for ** a ** fourth order ** boundary ** ´ ** value ** ** problem,** ” Discrete and Continuous Dynamical Systems Series ** A,** supplement, pp 662–671, 2005 ** A ** Cabada, M ... Problems, vol 2011, ** Article ** ID 893753, 18 pages, 2011 16 M R Grossinho, F M Minhos, and ** A ** I Santos, **A ** third order ** boundary ** ** value ** ** problem ** ** with ** one´ sided ** Nagumo ** condition,” Nonlinear Analysis: Theory,...

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... ** for ** some ** fourth-order ** ** boundary ** ** value ** problems,” Nonlinear Analysis Theory, Methods & Applications, vol 67, no 6, pp 1704–1709, 2007 G Chai, **Existence ** ** of ** ** positive ** ** solutions ** ** for ** ** fourth-order ** ** boundary ** ... a ** fourth-order ** ** boundary ** ** value ** ** problem,** ” Nonlinear Analysis Theory, Methods & Applications, vol 70, no 10, pp 3561–3566, 2009 Y Li, **Positive ** ** solutions ** ** of ** ** fourth-order ** ** boundary ** ** value ** problems ** with ** ... “Symmetric ** positive ** ** solutions ** ** for ** ** nonlocal ** ** boundary ** ** value ** problems ** of ** fourth order,” Nonlinear Analysis Theory, Methods & Applications, vol 68, no 3, pp 645–651, 2008 R Ma, **Existence ** ** of ** ** positive ** solutions...

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... existence ** and ** nonexistence ** of ** ** positive ** solutions to a class ** of ** third-order three-point ** nonhomogeneous ** BVP The authors in 12 studied the multiplicity ** of ** ** positive ** solutions for some ** fourth-order ** ... with ** nonhomogeneous ** boundary conditions II,” Journal ** of ** Mathematical Analysis ** and ** Applications, vol 330, no 2, pp 1393–1411, 2007 10 L Kong ** and ** Q Kong, **Uniqueness ** ** and ** ** parameter ** ** dependence ** ** of ** solutions ... unique ** positive ** ** solution ** ** of ** the BVP 1.5 – 1.7 The ﬁrst part ** of ** the theorem is proved In the rest ** of ** the proof, we will prove that such a ** positive ** ** solution ** uλ t satisﬁes properties P1 , P2 , and...

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... regular boundary value problems,” European Journal ** of ** Pure ** and ** Applied Mathematics, vol 1, no 2, pp 51–60, 2008 K R Mamedov ** and ** H Menken, **Asymptotic ** ** formulas ** ** for ** ** eigenvalues ** ** and ** ** eigenfunctions ** ** of ** ... Sturm-Liouville Operators ** and ** Applications, vol 22 ** of ** Operator Theory: Advances ** and ** Applications, Birkh¨ user, Basel, Switzerland, 1986 ** a ** M ** A ** Naimark, Linear Diﬀerential Operators Part 1, Frederick Ungar, New ... Case Assume that q x ∈ C 0, π ** and ** the condition q π − q / holds Based on the ** asymptotic ** expressions ** of ** the fundamental solutions ** of ** 1.1 ** and ** the ** asymptotic ** ** formulas ** ** for ** ** eigenvalues ** ** of ** the boundary-value...

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... 351–363, 2008 13 X Zhang, M Feng, and W Ge, “Symmetric ** positive ** ** solutions ** ** for ** ** p-Laplacian ** ** fourth-order ** diﬀerential ** equations ** ** with ** ** integral ** ** boundary ** conditions,” Journal of Computational and Applied ... X Zhang and L Liu, “A necessary and suﬃcient condition ** for ** ** positive ** ** solutions ** ** for ** ** fourth-order ** multi-point ** boundary ** value problems ** with ** ** p-Laplacian,** ” Nonlinear Analysis: Theory, Methods & Applications, ... smooth ** positive ** ** solutions ** to a class of ** singular ** m-point ** boundary ** value problems,” ** Boundary ** Value Problems, vol 2009, ** Article ** ID 191627, 13 pages, 2009 J R Graef and J R L Webb, “Third order boundary...

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... Journal ** of ** Mathematical Analysis and Applications, vol 314, no 1, pp 254–265, 2006 10 R Ma, **Nodal ** ** solutions ** ** of ** ** boundary ** ** value ** problems ** of ** ** fourth-order ** ordinary diﬀerential equations,” Journal ** of ** ... positive ** solutions ** ** of ** ** a ** ** fourth-order ** ** boundary ** ** value ** problem,” Applied Mathematics and Computation, vol 168, no 2, pp 1219–1231, 2005 R Ma, **Nodal ** ** solutions ** ** for ** ** a ** ** fourth-order ** ** two-point ** ** boundary ** ** value ** ... Computational and Applied Mathematics, vol 10, no 2, pp 203–217, 1984 R Ma and H P Wu, “Positive ** solutions ** ** of ** ** a ** ** fourth-order ** ** two-point ** ** boundary ** ** value ** problem,” Acta Mathematica Scientia ** A,** vol 22,...

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... theory ** of ** ** integral ** ** equations ** ** and ** their relation ** with ** boundaryvalue problems, we refer to the book ** of ** Corduneanu 22 ** and ** Agarwal ** and ** O’Regan 23 On the other hand, ** boundary-** value problems ** with ** ** integral ** ... paper, we consider the existence ** of ** ** positive ** ** solutions ** for a class ** of ** ** boundary ** value problems ** with ** ** integral ** ** boundary ** ** conditions ** ** of ** ** fourth-order ** ** impulsive ** diﬀerential ** equations:** f t, y t , φp y t ... studied ** boundary ** ** conditions ** corresponding to clamped ** and ** hinged ends ** and ** many nonlocal ** boundary ** ** conditions ** ** and ** established excellent existence results for ** multiple ** ** positive ** ** solutions ** ** of ** fourth-order...

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... Mathematics, Nanjing University ** of ** Aeronautics ** and ** Astronautics, Nanjing 210016, P R China ∗ Corresponding author: wang-fanglei@hotmail.com Email address: YA: anykna@nuaa.edu.cn Abstract This article ... ** Existence ** ** and ** ** multiplicity ** ** of ** ** solutions ** ** for ** ** a ** ** fourth-order ** ** elliptic ** equation Fanglei Wang∗1 ** and ** Yukun An2 College Department ** of ** Science, Hohai University, Nanjing, 210098, P R China ** of ** Mathematics, ... References [1] Ma, TF: ** Existence ** results ** for ** ** a ** model ** of ** nonlinear beam on elastic bearings Appl Math Lett 13, 11–15 (2000) [2] Ma, TF: ** Existence ** results ** and ** numerical ** solutions ** ** for ** ** a ** beam equation with...

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... ** Existence ** ** of ** ** positive ** ** solutions ** ** for ** ** fourth-order ** ** semipositone ** ** multi-point ** ** boundary ** ** value ** ** problems ** ** with ** ** a ** ** sign-changing ** ** nonlinear ** term Yan Sun Department ** of ** Mathematics, Shanghai Normal University, ... [7] Gupta, CP: Solvability ** of ** ** a ** three-point ** nonlinear ** ** boundary ** ** value ** ** problems ** ** for ** ** a ** second order ordinary diﬀerential equation J Math Anal Appl 168, 540–551 (1992) 23 [8] Gupta, CP: ** A ** sharp condition ... problem at resonance ** Nonlinear ** Anal 24(10), 1483–1489 (1995) [5] Gupta, CP, Ntouyas, SK, Tsamatos, P: On an m-point ** boundary ** ** value ** problem ** for ** second-order ordinary diﬀerential equations ** Nonlinear ** Anal...

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... estimates on multiple ** solutions ** ** of ** ** Lidstone ** boundary value problems,” Acta Mathematica Hungarica, vol 86, no 1-2, pp 137–168, 2000 16 P J Y Wong ** and ** R P Agarwal, “Characterization ** of ** eigenvalues ** for ** ... equations,” Lithuanian Mathematical Journal, vol 49, no 1, pp 71–92, 2009 11 D R Anderson ** and ** F Minhos, **A ** ** discrete ** ** fourth-order ** ** Lidstone ** ** problem ** ** with ** parameters,” Applied ´ Mathematics ** and ** Computation, ... He ** and ** Y Su, “On ** discrete ** ** fourth-order ** boundary value problems ** with ** three parameters,” Journal ** of ** Computational ** and ** Applied Mathematics, vol 233, no 10, pp 2506–2520, 2010 13 R P Agarwal and...

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... ** and ** Computation, vol 203, no 1, pp 30–38, 2008 20 D Bai ** and ** Y Xu, “Nontrivial ** solutions ** ** of ** ** boundary ** ** value ** problems ** of ** second-order diﬀerence equations,” Journal ** of ** Mathematical Analysis ** and ** Applications, ... to deal with ** the ** ** existence ** ** of ** ** solutions ** ** for ** ** the ** ** boundary ** ** value ** problems ** of ** ** fourth-order ** diﬀerential equations Because ** of ** applications in many areas ** for ** diﬀerence equations, in recent years, there ... Z Bai ** and ** H Wang, **On ** positive ** solutions ** ** of ** some nonlinear ** fourth-order ** beam equations,” Journal ** of ** Mathematical Analysis ** and ** Applications, vol 270, no 2, pp 357–368, 2002 Q Yao, “Positive solutions...

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... Krasnoselskii’s theorem ** of ** cone expansion/compression type has been used to study the ** existence ** ** of ** ** positive ** ** solutions ** ** of ** ** boundary ** ** value ** ** problems ** in many papers; ** Chuanzhi ** Bai see, ** for ** example, Liu [7], ... multiplicity ** of ** ** solutions ** ** of ** a kind ** of ** ** fourth-order ** ** boundary ** ** value ** problem,” Nonlinear Analysis: Theory, Methods & Applications, vol 62, no 5, pp 803–816, 2005 [7] B Liu, **Positive ** ** solutions ** ** of ** ** fourth-order ** ... two-point ** boundary ** ** value ** ** problems,** ” Electronic Journal ** of ** Diﬀerential Equations, no 16, pp 1–8, 2007 [9] R Ma, **Positive ** ** solutions ** ** of ** ** fourth-order ** two-point ** boundary ** ** value ** ** problems,** ” Annals ** of ** Differential...

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