變分法在時標上二階Sturm-Liouville邊值問題中的應用.pdf

1、蘭州大學碩士學位論文變分法在時標上二階SturmLiouville邊值問題中的應用姓名：張全國申請學位級別：碩士專業(yè)：基礎數(shù)學指導教師：孫紅蕊20100501AbstractInthispaper，usingvariationalmethods，weconsideraclassofsecondor—derSturm—LiouvilleboundaryvalueproblemswithpositiveparameterAontimesca

2、les一(p(￡)u△(￡))△q(￡)亂。(￡)=Af(t，u盯(￡))，t∈【0，丁】，Ql札(o)一Ct2U△(o)=0，Q3u(盯2(丁))OL4U△(盯(丁))=0InChapter2，weresearchtheexistenceofsolutionsfor(R)InSection1，wecon—structthecorrespondingvariationalframeworkfortheproblem(R)andprese

3、ntthepropertiesofvariationalframeworkInSection2，weconsiderthesecondor—derSturm—LiouvilleeigenvaluesproblemsandgivethecharacterizationofthefirsteigenvalueinSobolevspace，then，weprovetheexistenceinterva，lofAsuchthattimprobl

4、em(R)hasoneortwosolutionbydirectvariationalmethod，MountainpusslemmaandthecriticalpointtheoremofBrezisandNirenbergInSection3，wederivetimexistenceofthreesolutionsof(R)when入liesinasuitablein—tervalbyusingathreecriticalpoint

5、theoremBonannoandCanditoestablishedFinally，wegivesomeexamplestoillustrateOllrresultsinSection4InChapter3，westudytheexistenceofpositivesolutionsfor(足)InSection1，weprovetheexistenceofpositivesolutionsfor(，久)isequiwflenttoe

6、xistenceofsolutionsforthefollowingboundaryvahmproblemswhenthenonlineartermsatisfiesthat廠(f，0)ispositiveandp(t)isnon—decreasingJ一(p(￡)u△(￡))△q(t)u4(z)=Af(t，(u)盯(￡))t∈(0，丁】，【Q1札(o)一Of2l／△(o)=0，OL37／(0“2(丁))a4讓△(盯(丁))=0Then

7、，weconstructthecorrespondingvariationalframeworkfortheproblem(哎)andpresentthepropertiesofvariationalframeworkInSection2，wederivetheexistenceofpositivesolutionsof(片)whenAliesinasuitableintervalbydirectvariationalmethodand