| MULTIBUMP SOLUTIONS AND CRITICAL GROUPS | |
| Arioli, Gianni ; Szulkin, Andrzej ; Zou, Wenming | |
| 2010-10-12 ; 2010-10-12 | |
| 关键词 | Multibump solution critical group Bernoulli shift Newtonian system Schrodinger equation critical exponent PERIODIC SCHRODINGER-EQUATIONS CRITICAL SOBOLEV EXPONENT HAMILTONIAN SYSTEM HOMOCLINIC ORBITS EXISTENCE R(N) Mathematics |
| 中文摘要 | We consider the Newtonian system -q + B(t)q = W-q(q, t) with B, W periodic in t, B positive definite, and show that for each isolated homoclinic solution q(0) having a nontrivial critical group ( in the sense of Morse theory), multibump solutions ( with 2 <= k <= infinity bumps) can be constructed by gluing translates of q(0). Further we show that the collection of multibumps is semiconjugate to the Bernoulli shift. Next we consider the Schrodinger equation -Delta u + V(x)u = g(x, u) in R-N, where V, g are periodic in x(1),..., x(N), sigma(-Delta + V) subset of (0, infinity), and we show that similar results hold in this case as well. In particular, if g(x, u) = vertical bar u vertical bar(2)*(-2)u, N >= 4 and V changes sign, then there exists a solution minimizing the associated functional on the Nehari manifold. This solution gives rise to multibumps if it is isolated. |
| 语种 | 英语 ; 英语 |
| 出版者 | AMER MATHEMATICAL SOC ; PROVIDENCE ; 201 CHARLES ST, PROVIDENCE, RI 02940-2213 USA |
| 内容类型 | 期刊论文 |
| 源URL | [http://hdl.handle.net/123456789/81321]  |
| 专题 | 清华大学 |
| 推荐引用方式 GB/T 7714 | Arioli, Gianni,Szulkin, Andrzej,Zou, Wenming. MULTIBUMP SOLUTIONS AND CRITICAL GROUPS[J],2010, 2010. |
| APA | Arioli, Gianni,Szulkin, Andrzej,&Zou, Wenming.(2010).MULTIBUMP SOLUTIONS AND CRITICAL GROUPS.. |
| MLA | Arioli, Gianni,et al."MULTIBUMP SOLUTIONS AND CRITICAL GROUPS".(2010). |
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