Imed Bachar: Time-independent Schrödinger polyharmonic equation and applications, p.163-179

Abstract:

We prove that the time-independent Schrödinger polyharmonic equation $% \left( -\Delta \right) ^{m}u+q\left( x\right) u=\psi \left( x\right) >0,$ $% x\in D,$ where $D$ is an unbounded domain of $\mathbb{R}^{n}\left( n\geq 2\right)$ has a positive solution provided that the function $q$ belongs to a certain Kato class of functions $K_{m,n}^{\infty }\left( D\right) .$ As applications, the existence and asymptotic behavior of positive solutions of some polyharmonic problems are established.

Key Words: Schrödinger polyharmonic equation, Green function, polyharmonic elliptic equation, positive solution.

2000 Mathematics Subject Classification: Primary: 34B27
16T05;
Secondary: 35J40.

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