兩類帶有非局部項的偏微分方程解的存在性.pdf

1、Thesis for Master’s Degree, Shanxi University, 2016Existence of Solutions to Two Classes of Partial Differential Equations with Nonlocal TermS tu de nt Na meS u pe r vis orM a j o rFie l d o f Re s e a r c h D e pa r tm

2、 e nt Re s e a r c h D u r a tio nHong Gu o Yu hu aLiFu nda me nta lMa the ma tic sNonl ine a rFu nc tiona lAna l y s isS c hoolof Ma the ma tic a lS c ie nc e s2013.09-2016.06June, 2016兩類帶有非局部項的偏微分方程解的存在性C onte ntsA b s

3、 tr a c t in Chine s e.............................................................................................................. IA b s tr a c t in E ngl is h .......................................................

4、..................................................... IIIC ha pte r1 Exis te nc eo f s ign-c ha nging s ol u tionsto ac l a s so f K ir c h h o ff e qu a ­tio n w ith a n e xpone ntia ls ou r c e................

5、..................................................................... 1§1.1 Intr odu c tion............................................................................................................ 1§1.2 P

6、r e l imina r ie s......................................................................................................... 3§1.3 Thepr oof of thema in r e s u l ts .................................................

7、............................12C ha pte r2 Exis te nc eo f s ol u tionsto ak ind o f s e c ond ha r m onice qu a tio n .. 14§2.1 Intr odu c tion .....................................................................

8、.................................... 14§2.2 Pr e l imina r ie s....................................................................................................... 15§2.3 Thepr oof of thema in r e s u l ts

9、 .............................................................................20Re fe r e nc e s............................................................................................................................

10、.. 22Re s e a r c h a c hie ve me nts....................................................................................................... 24Ac k nowl e dge m e nt ......................................................

11、.......................................................... 25Pe r s ona lp r o fil e s ................................................................................................................... 26L e tte ro f c

12、om m itm e n t.........................................................................................................27A u th o r iza tio n s ta te m e nt ..............................................................