11142.兩類擬線性薛定諤方程解的存在性和集中性研究

1、兩類擬線性薛定諤方程解的存在性和集中性研究ExistenceandconcentrationofsolutionsfortwoclassesofquasilinearSchrSdingerequations作者：馮鵬濤Author：!里墜g羔壘旦里皇墜g指導(dǎo)教師：沈自飛Supervisor：圣選i曼墾竺里專業(yè)：基礎(chǔ)數(shù)學(xué)學(xué)位：理學(xué)碩士授予單位：浙江師范大學(xué)Major：里墜堡叢堂塾竺里煎i望Degree：叢箜主曼!竺!曼墮旦墨塑Instit

2、ute：圣墮自i壘翌g盟旦!里墾!型望i翌!墨i!YMay2016ExistenceandCOnCentratiOnofsolutionsfortwoclassesofquasilinearSchr6dingerequationsABSTRACTInthisarticleweprovetheexistenceofpositivegroundstatesolutionsfortwokindsofquasilinearSchrodinger

3、equation，andgivesomepropertiesabouttheirsolu—tionsWeconsiderthefollowingtwocasesThefirstcase：WestudyaquasilinearSchr6dingerequationoftheform△t‘v(x)u—A(u2)“=h(x，札)，z∈RⅣ，(1)andconsidertheexistenceandmultiplicityofitssoluti

4、on，whereitsnonlinearityisperiodicasymptoticallylinearandsatisfiesamonotonicityconditionWeusethegen—eralizedNeharimanifoldmethodstoobtainagroundstatesolutionandinfinitelymanygeometricallydistinctsolutionswhenthenonlineari

5、tyisoddTheSecondcase：westudytheexistenceofnontrivialsolutionsforthefollowingquasilinearSchr6dingerequation—E2△札v(x)u—E2[△(122)】“Q(z)九(扎)，z∈腿2inthewholetwodimensionwhereVandQaretwocontinuousrealfunctionon酞2Thenonlinearity

6、hisallowedtoenjoythecriticalexponentialgrowthinR2wearegoingtousetheTrudingerMoserinequationandmountainpasslemmatostudytheexistenceofsemiclassicalgroundstatesolutionsfor￡smallanddescribecertaincon—centrationphenomenaofthe