一类拟线性 schrdinger 方程解的存在性研究

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1、᪥ṹ：10285：20134207031ắᦻ(）ឋSchr6dingerḄᙠឋẆOntheExistenceofSolutionsforQuasilinear__________SchrodingerEquations__________Ẇ_________________ᢣᦟ!"#$%&ᦪẆᔣ)ឋ*+ᑖ᪆ᡠᙠ▾0ᦪ1▾ᦻ2345201664ᨴ万方数据万方数据89ᜧᦻ;<ឋ=>?@AB=>：ᡠ23ḄᦻD?@ᙠ!ḄᢣE，;GHIẆJKᡠLMḄᡂO。◀ᦻRSTU>VᵨḄᑁY᜜，

2、?ᦻ[ᐸ^_@ᡈabSTc⊤ᡈeᑏgḄẆᡂO，h[ijM89ᜧᡈᐸkᦟlm᪀ḄopqrᵨgḄᩞᧇ。u?ᦻḄẆKvB⌕xyḄ_@zab，ᙳSᙠᦻR

3、>}~᪗>。?@?=>Ḅ。曰o$ᦻKὅ：万方数据万方数据89ᜧᦻrᵨᣴᩗ=>?@ᐰ89ᜧᐵᦈa、zrᵨᦻḄ，ᓽ：ᦻ℉Kᩗ89ᜧ。?ᦻᵯᦻ᫏ḄᑁYzᦻḄᑁY。89ᜧᨵᩗᔣ ¡¢p✂、R ¤1▾ᦻy¥¦§¨R©、R 1ᢈ¥¦Ẇᡠ（¬ᦪᵯv᱐¤)、R 5°（ᐝ²᱐）ᵯᩖ´¤〈3?ᦻḄ¶ᓺ¸zᵯᦻ᫏，ᐕºᦻ»¼▅z¾▅，¿

4、ÀᵨÁᓺ、Âᓺᡈᐸ^¶ᑴÄÅ

5、zÆÇᦻ，¿

6、ÈᦻḄᐰ0ᡈ0ᑖᑁYÇᐭᨵᐵᦪÊHIËÌ。ÍÎᦻÏ?ᦻᙠ_____6—ᨴÎÐ〉ᵨ?。)ÍÎᦻ□ᦻKὅ:45：B>!:45：万方数据万方数据ឋSchr6dingerḄᙠឋẆ᤺⌕᤺⌕ᦻᑭᵨᑖẆឋSchr6dinger—An+V(x)u--uAu2=h(x,u),xGQ,{u=0,xGdQ%&'(Ḅ*ᙠឋ，ᐸ.Q/.Ḅᐝ123（ᨵ6ᡈ86)，h(x,u)Ḅ?@Aᦪ.ᡃEḄFGH⌕ᒹKL☢NOPᑖ：、Sn<(N>3).Ḅᨵ6ᐝ123，V(x)V0(xGQ),h(x,u)=f(x,u)+

7、Xg(u)X,ᡃEᑭᵨYZAᦪᢈ]^ᔠᦻ`[21]Ḅ^cdefghᐙᑖjḄᐭ,>k*ᙠl(mn(,opf(x,u)qrs▲ᑴvwᩩyḄ?@Aᦪ,ᐭ/lzᦪ,g(u)/{PH61der?@ḄAᦪ.Ḅ/ᡃEὃ⇋Ḅ⚪.Aᦪh(x,u)sqrᐺḄ（AR)ᩩy.、SQ=Rn(N>3),V(x)=0(xGQ),h(x,u)=K(x)

8、u

9、p-2uX,ᡃEᑭᵨNehari᡾ᢈ,f>kḄOl(,ᐸ.4

10、Nehari.Gὅ：¥¦ᢣ¨ὁª：«¬ᦟᣴI万方数据AbstractOntheExistenceofSolutionsforQuasilinearEllipticEquationsAbstractInthisthesis,byusingvariationalmethods,westudytheexistenceofnontrivialsolutionsofaclassquasilinearellipticequations—Au+V(x)u—-uAu2=h(x,u),xGQ,u=0,xGdQ,whereQisasmoothdomain(boundedorunbounde

11、d)inRN,h(x,u)iscontinuousonQxR.Ourresultsobtainedinthethesisareincludedinthefollowingtwoparts:InPart1,whenQisaboundeddomaininRN(N>3),V(x)V0(xGQ),h(x,u)=f(x,u)+Ag(u),byusingthecut-offfunctiontechniquecombiningwiththeresultin[21],weshowthattheequationhasapositivesolutionandanegativesolution

12、forᐭ〉0small,wheref(x,u)GC(QxR)satisfyingsomerestrictedgrowthconditions,ᐭisapositiveparameter,andg(u)isalocallyHoldercontinuousfunction.Wepointoutthath(x,u)heremaynotsatisfytheclassical(AR)condition.InPart2,whenQ=RN(N>3),V(x)=0(xGQ),h(x,u)=K(x)

13、u

14、p-2u,weobtainapositi