具共振條件下多點(diǎn)邊值問題解的存在性.pdf

1、華中科技大學(xué)碩士學(xué)位論文具共振條件下多點(diǎn)邊值問題解的存在性姓名：張祖峰申請學(xué)位級別：碩士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：劉斌20070513AbstractThe ordinary differential equation boundary value problem is one of the most im-portant branches of ordinary differential equations. It is resulte

2、d from physics, chem-istry, biology, medicine, economics, engineering, cybernetics and so on. Boundary valueproblem at resonance have been studied by several authors in recent ten years. But theexistence of high-order wi

3、th complex boundary value conditons and equation includingp-Laplacian operator has rarely been studied. So in this paper, we consider the prob-lem as following: In section 1, we give an introduction of the origin of the

4、problems,the status of the research on related issues, and the trend of the future development.In section 2, result for solvability of 4-point boundary value problems of fourth orderdifferential problem at resonance is o

5、btained by using coincidence degree theory dueto Mawhin. An sufficient condition is given under non-linear growth restriction on f.In section 3, we study the existence of p-Laplace-like equtions subject to multi-pointbou

6、ndary value problems at resonance. By using degree theory, we obtained two suf-ficient conditions for solvability, some known results are improved. In section 4, weuse Brouwer degree and Leray-Schauder degree to discuss

7、solvability of multi-pointboundary value problem with two critical conditions. the methods used in the paperare different from some known results.Later, we can consider boundary value problem at resonance with different