Acta mathematica scientia,Series A ›› 2000, Vol. 20 ›› Issue (2): 202-209.
• Articles • Previous Articles Next Articles
Online:
Published:
Abstract:
We consider Dirichlet problem for mean curvature type equation with singular term and positive parameter ε and prove that the above problem has at least a classical solution for εsmall enough and has no calssical solution for εlarge enough.
Key words: Ｍｅａｎｃｕｒｖａｔｕｒｅｔｙｐｅｅｑｕａｔｉｏｎ, Ｄｉｒｉｃｈｌｅｔｐｒｏｂｌｅｍ, Ｃｌａｓｓｉｃａｌｓｏｌｕｔｉｏｎ．
CLC Number:
Dai Qiuyi. Dirichlet Problem for Mean Curvature Type Equation with Singular Term[J].Acta mathematica scientia,Series A, 2000, 20(2): 202-209.
0 / / Recommend
Add to citation manager EndNote|Reference Manager|ProCite|BibTeX|RefWorks
URL: http://121.43.60.238/sxwlxbA/EN/
http://121.43.60.238/sxwlxbA/EN/Y2000/V20/I2/202
１ ＪｏｓｅｐｈＤＤ，ＬｕｎｄｇｒｅｎＴＳ．Ｑｕａｓｉｌｉｎｅａｒｄｉｒｉｃｈｌｅｔｐｒｏｂｌｅｍｓｄｒｉｖｅｎｂｙｐｏｓｉｔｉｖｅｓｏｕｒｃｅｓ．ＡｒｃｈＲａｔＭｅｃｈＡｎａｌ，１９９３，４９：２４１－２６９ ２ ＢｏｂｉｓｕｄＬＥ．Ａｓｙｍｐｔｏｔｉｃｄｅａｄｃｏｒｅｓｆｏｒｒｅａｃｔｉｏｎｄｉｆｆｕｓｉｏｎｅｑｕａｔｉｏｎｓ．ＪＭａｔｈＡｎａｌＡｐｐｌ，１９９０，１４７：２４９－２６２ ３ ＢｏｂｉｓｕｄＬＥ．ＢｅｈａｖｉｏｒｏｆｓｏｌｕｔｉｏｎｓｆｏｒａＲｏｂｉｎｐｒｏｂｌｅｍ．ＪＤｉｆｆｅｒＥｑｕ，１９９０，８５：９１－１０４ ４ ＢａｘｌｅｙＪＶ．Ｓｏｍｅｓｉｎｇｕｌａｒｎｏｎｌｉｎｅａｒｂｏｕｎｄａｒｙｖａｌｕｅｐｒｏｂｌｅｍ．ＳＩＡＭＪＭａｔｈＡｎａｌ，１９９１，２２：４６３－４７９ ５ ＢａｘｌｅｙＪＶ．Ｓｉｎｇｕｌａｒｒｅａｃｔｉｏｎｄｉｆｆｕｓｉｏｎｂｏｕｎｄａｒｙｖａｌｕｅｐｒｏｂｌｅｍｓ．ＪＤｉｆｆｅｒＥｑｕ，１９９５，１１５：４４１－４５７ ６ ＫａｗａｒａｄａＨ．ＯｎｔｈｅｓｏｌｕｔｉｏｎｏｆｉｎｉｔｉａｌｂｏｕｎｄａｒｙｖａｌｕｅｐｒｏｂｌｅｍｆｏｒUt－Uxx＝1/1-UＰｕｂｌ．ＲＩＭＳ，ＫｙｏｔｏＵｎｉｖ，１９７５，１０： ７２９－７３６ ７ ＡｃｋｅｒＡ，Ｗａｌｔｅｒ Ｗ．Ｔｈｅｑｕｅｎｃｈｉｎｇｐｒｏｂｌｅｍｆｏｒｎｏｎｌｉｎｅａｒｐａｒａｂｏｌｉｃｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｓ．Ｌｅｃｔｕｒｅ Ｎｏｔｅｓｉｎ Ｍａｔｈ，１９７６，５６４：１－１２ ８ ＤｚｉｕｋＧ，ＫａｗｏｈｌＢ．Ｏｎｒｏｔａｔｉｏｎａｌｌｙｓｙｍｍｅｔｒｉｃｍｅａｎｃｕｒｖａｔｕｒｅｆｌｏｗ．ＪＤｉｆｆｅｒＥｑｕ，１９９１，９３：１４２－１４９ ９ ＬｅｖｉｎｅＨ Ａ．Ａｄｖａｎｃｅｓｉｎｑｕｅｎｃｈｉｎｇ，ＰｒｏｇｒｅｓｓｉｎＮｏｎｌｉｎｅａｒＤｉｆｆｅｒｅｎｔｉａｌＥｑｕａｔｉｏｎｓａｎｄＴｈｅｉｒＡｐｐｌｉｃａｔｉｏｎｓ．Ｂｉｒｋｈ¨ａｕｓｅｒＢｏｓｔｏｎ，１９９２，７：３１９－３４６ １０ ＧｉｌｂａｒｇＤ，ＴｒｕｄｉｎｇｅｒＮＳ．Ｅｌｌｉｐｔｉｃｐａｒｔｉａｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｓｏｆｓｅｃｏｎｄｏｒｄｅｒ．Ｎｅｗ Ｙｏｒｋ：ＳｐｒｉｎｇｅｒＶｅｒｌａｇ，１９８３ １１ ＤｕｇｕｎｄｊｉＪ，ＧｒａｎａｓＡ．ＦｉｘｅｄＰｏｉｎｔＴｈｅｏｒｙ．ＭｏｎｏｇｒａｆｉｅＭａｔｈ，ＴＯＭ６１，Ｗａｒｓｚａｗａ，１９８２ １２ ＢｅｒｅｓｔｙｃｋｉＨ，ＮｉｒｅｎｂｅｒｇＬ．Ｏｎｔｈｅｍｅｔｈｏｄｏｆｍｏｖｉｎｇｐｌａｎｅｓａｎｄｔｈｅｓｌｉｄｉｎｇｍｅｔｈｏｄ．ＢｏｌＳｏｃＢｒａｓＭａｔ，１９９１，２２（１）：１－３７ １３ ＬａｄｙｚｅｎｓｋａｊａＯ Ａ，ＳｏｌｏｎｎｉｋｏｖＶ Ａ，ＵｒａｌｃｅｖａＮ Ｎ．Ｌｉｎｅａｒａｎｄｑｕａｓｉｌｉｎｅａｒｅｑｕａｔｉｏｎｓｏｆｐａｒａｂｏｌｉｃｔｙｐｅ．Ａｍｅｒ ＭａｔｈＳｏｃＴｒａｎｓｌａｔｉｏｎｓｏｆＭａｔｈｅｍａｔｉｃａｌＭｏｎｏｇｒａｐｈｙ．１９６８，Ｎｏ．２３
Cited
Global Structure of Positive Solutions of Singular Nonlinear Sturm-Liouville Problems