摘要
We consider the boundary value problem△u＋︳x︳^2α︳u︳p-1u=0,-1〈α≠0.in the unit ballB with the homogeneous Dirichlet boundary condition, when p is a large exponent. By a constructive way, weprove that for any positive integer m, there exists a multi-peak nodal solution vp whose maxima and minima arelocated alternately near the origin and the other m points q1=（λcos^2Л（1-1）/m,λsin 2Л（1-1）/m,1=2,…,m＋1such that as p goes to ＋∞ ,p︳x︳2α︳up︳p-1 up→8Лe（1＋α）（1＋α）δ0＋∑^m＋1δ_1=28Лe（-1）l-1δql,whereλ∈（0, 1）, m is an odd number with（1＋α）（m＋2） -- 1 〉 0, or m is an even number. The same techniqueslead also to a more general result on general domains.
We consider the boundary value problem△u＋︳x︳^2α︳u︳p-1u=0,-1〈α≠0.in the unit ballB with the homogeneous Dirichlet boundary condition, when p is a large exponent. By a constructive way, weprove that for any positive integer m, there exists a multi-peak nodal solution vp whose maxima and minima arelocated alternately near the origin and the other m points q1=（λcos^2Л（1-1）/m,λsin 2Л（1-1）/m,1=2,…,m＋1such that as p goes to ＋∞ ,p︳x︳2α︳up︳p-1 up→8Лe（1＋α）（1＋α）δ0＋∑^m＋1δ_1=28Лe（-1）l-1δql,whereλ∈（0, 1）, m is an odd number with（1＋α）（m＋2） -- 1 〉 0, or m is an even number. The same techniqueslead also to a more general result on general domains.
基金
Supported by the National Natural Science Foundation of China(No.11171214)
