TAILIEUCHUNG - Báo cáo hóa học: "Research Article Global Behavior of the Components for the Second Order m-Point Boundary Value Problems"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Global Behavior of the Components for the Second Order m-Point Boundary Value Problems | Hindawi Publishing Corporation Boundary Value Problems Volume 2008 Article ID 254593 10 pages doi 2008 254593 Research Article Global Behavior of the Components for the Second Order m-Point Boundary Value Problems Yulian An1 2 and Ruyun Ma1 1 Department of Mathematics Northwest Normal University Lanzhou 730070 China 2 Department of Mathematics Lanzhou Jiaotong University Lanzhou 730070 China Correspondence should be addressed to Yulian An an_yulian@ Received 9 October 2007 Accepted 16 December 2007 Recommended by Kanishka Perera We consider the nonlinear eigenvalue problems u rf u 0 0 t 1 u 0 0 u 1 ymAa-iufnf where m 3 n e 0 1 and ai 0 for i 1 . m - 2 with y m-Ai 1 r e R f e C1 R R . There exist two constants s2 0 s1 such that f s1 f s2 f 0 0 and f0 limup0 f ù ù e 0 to fTO lim u PTO f ù ù e 0 to . Using the global bifurcation techniques we study the global behavior of the components of nodal solutions of the above problems. Copyright 2008 Y. An and R. Ma. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. Introduction In 1 Ma and Thompson were concerned with determining values of real parameter r for which there exist nodal solutions of the boundary value problems u ra f f u 0 0 t 1 L _ I u 0 u 1 0 where a and f satisfy the following assumptions H1 f e C R R with sf s 0 for s 0 H2 there exist f0 fTO e 0 to such that f0 lim ỉ t fTO lim f st s p0 s s pto s H3 a 0 1 p 0 to is continuous and a t 0 on any subinterval of 0 1 . Using Rabinowitz global bifurcation theorem Ma and Thompson established the following theorem. 2 Boundary Value Problems Theorem . Let H1 H2 and H3 hold. Assume that for some k G N either k Xk r L3 fw f0 or Xk Xk f0 r fW 1-4 Then have two solutions u and u- such that u has exactly k - 1 zeros in 0 1 and is positive near 0 and U- has exactly k - 1 zeros in 0 1

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