本文選題：乘積空間 + m增生映射�。� 參考：《數(shù)學(xué)雜志》2017年02期

【摘要】：本文研究了一類capillarity系統(tǒng)解的存在性問題.采用在乘積空間中定義非線性映射的方法,把capillarity系統(tǒng)轉(zhuǎn)化為非線性算子方程.借助于Sobolev嵌入定理等技巧證明非線性映射具有緊性,進(jìn)而利用非線性映射值域的性質(zhì)得到非線性算子方程解的存在性的結(jié)論.并由此獲得在一定條件下capillarity系統(tǒng)在L~(P1)(Ω)×L~(P2)(Ω)×…×L~(PM)(Ω)空間中存在非平凡解的結(jié)論,其中Ω為R~N(N≥1)中有界錐形區(qū)域且2N/N+1p_i+∞,i=1,2,…,M.本文所研究的問題和所采用的方法推廣和補(bǔ)充了以往的相關(guān)研究工作.
[Abstract]:In this paper, we study the existence of solutions for a class of capillarity systems. By using the method of defining nonlinear mapping in the product space, the capillarity system is transformed into a nonlinear operator equation. By means of Sobolev embedding theorem, the compactness of nonlinear maps is proved, and the existence of solutions of nonlinear operator equations is obtained by using the properties of the range of nonlinear mappings. Under certain conditions, it is obtained that the capillarity system can be used in LP1 (惟) 脳 L ~ (2 +) P ~ (2 +) (惟) 脳. A conclusion on the existence of nontrivial solutions in a 脳 L ~ (1) PMN (惟) space, where 惟 is a bounded conical domain in R~N(N 鈮，

本文編號(hào)：1892701