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研究生:夏文茵
研究生(外文):Wen-Yin Hsia
論文名稱:一維推廣Ambrosetti-Brezis-Cerami問題解集合的結構
論文名稱(外文):The Structure of the Solution Set of a Generalized Ambrosetti-Brezis-Cerami Problem in One Space Variable
指導教授:王信華
指導教授(外文):Shin-Hwa Wang
學位類別:碩士
校院名稱:國立清華大學
系所名稱:數學系
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2004
畢業學年度:92
語文別:英文
論文頁數:20
中文關鍵詞:解集合多重正解分支凹凸非線性時間圖
外文關鍵詞:solution setexact multiplicitypositive solutionbifurcationconcave-convex nonlinearitytime map
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  • 被引用被引用:0
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  • 下載下載:3
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我們探討非線性兩點邊界值問題的解集合的結構,當滿足一些條件的時候.在(A1)-(A4)的條件之下,我們可以證明存在某一個正數使得這個問題當介在0跟正數之間會有兩個正解,當等於正數之時只有一個正解,當大於正數之時會沒有正解.
1. Introduction……………………….. 2
2. Main Results………………………. 4
3. Lemmas……………………………11
4. Proofs of Main Results…………….12
References……………………………19
[1]I. Addou, A. Benmezai, S. M. Bouguima and M. Derhab, Exactness results for generalized Ambrosetti-Brezis-Cerami problem and related one-dimensional elliptic equations, Electron. J. Diff. Eqns.(2000), 1-34.
[2]A. Ambrosetti, H. Brezis and G. Cerami, Combined effects of concave and convex nonlinearities in some elliptic problems, J. Funct. Anal.{122} (1994), 519-543.
[3]M. G. Crandall and P. H. Rabinowitz, Bifurcation, perturbation of simple eigenvalues and linearized stability, Arch. Rational Mech. Anal.{52} (1973), 161--180.
[4]B. Gidas, W. N. Ni and L. Nirenberg, Symmetry and related properties via the maximum principle, Comm. Math. Phys.{68} (1979), 209-243.
[5]P. Korman, On uniqueness of positive solutions for a class of semilinear equations,Discrete Contin. Dyn. Syst.8 (2002), 865--871.
[6]P. Korman and J. Shi, Instability and exact multiplicity of solutions of semilinear equations, Electron. J. Diff. Eqns. Conf., 5 (2000), 311--322.
[7]T. Laetsch, The number of solutions of a nonlinear two point boundary value problem, Indiana Univ. Math. J.{20} (1970), 1-13.
[8]J. Sanchez and P. Ubilla, One-dimensional elliptic equation with concave and convex nonlinearities, Electron. J. Diff. Eqns.{2000} (2000), 1-9.
[9]J. Shi, private communications.
[10]M. Tang, Exact multiplicity for semilinear Dirichlet problem involving concave and convex nonlinearities, Proc. Royal Soc. Edinburgh, Sect. A., {133} (2003), 705--717.
[11]S.-H. Wang and T.-S. Yeh, On the exact structure of positive solutions of an Ambrosetti-Brezis-Cerami problem and its generalization in one space variable, {Differential Integral Equations, }in press.
[12]S.-H. Wang and T.-S. Yeh, Exact multiplicity and ordering properties of positive solutions of a p-Laplacian dirichlet problem and their applications, J. Math. Anal. Appl.,in press.
[13]S.-H. Wang and T.-S. Yeh, A complete classification of bifurcation diagrams of a Dirichlet problem with concave-convex nonlinearities, to appear in J. Math. Anal. Appl. (under minor revisions).
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