The eigenvalue distribution for a degenerate elliptic operator — div {(1−|x|2)grad·}

1990 ◽  
Vol 71 (1) ◽  
pp. 17-27
Author(s):  
Yoichi Miyazaki
Keyword(s):  
Elliptic Operator ◽  
Eigenvalue Distribution ◽  
Degenerate Elliptic Operator ◽  
Degenerate Elliptic

Infinitely many solutions for semilinear Δλ-Laplace equations with sign-changing potential and nonlinearity

2017 ◽  
Vol 54 (4) ◽  
pp. 536-549 ◽  
Author(s):  
Jianhua Chen ◽  
Xianhua Tang ◽  
Zu Gao
Keyword(s):  
Elliptic Operator ◽  
Bounded Domain ◽  
Boundary Value ◽  
Quadratic Growth ◽  
Infinitely Many Solutions ◽  
Type Condition ◽  
Degenerate Elliptic Operator ◽  
Laplace Equations ◽  
Degenerate Elliptic ◽  
Strongly Degenerate

In this paper, we prove the existence of infinitely many solutions for the following class of boundary value elliptic problems where Ω is a bounded domain in RN (N ≥ 2), Δλ is a strongly degenerate elliptic operator, V (x) is allowing to be sign-changing and f is a function with a more general super-quadratic growth, which is weaker than the Ambrosetti-Rabinowitz type condition.

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