scholarly journals Multiple sign-changing solutions of an elliptic eigenvalue problem

2005 ◽  
Vol 12 (4) ◽  
pp. 737-746 ◽  
Author(s):  
Aixia Qian ◽  
◽  
Shujie Li ◽  
Keyword(s):  
Eigenvalue Problem ◽  
Elliptic Eigenvalue Problem ◽  
Sign Changing Solutions

MULTIPLE SIGN CHANGING SOLUTIONS OF A QUASILINEAR ELLIPTIC EIGENVALUE PROBLEM INVOLVING THE p-LAPLACIAN

2004 ◽  
Vol 06 (02) ◽  
pp. 245-258 ◽  
Author(s):  
THOMAS BARTSCH ◽  
ZHAOLI LIU
Keyword(s):  
Eigenvalue Problem ◽  
Smooth Domain ◽  
Oscillatory Behaviour ◽  
Bounded Smooth Domain ◽  
Elliptic Eigenvalue Problem ◽  
Positive Multiple ◽  
Bounded Smooth ◽  
Sign Changing Solutions ◽  
Quasilinear Elliptic

We consider the eigenvalue problem [Formula: see text] where Ω⊂ℝN is a bounded smooth domain and Δpu denotes the p-Laplacian, 1<p<+∞; λ>0 is a parameter. The nonlinearity f is required to have an oscillatory behaviour. We prove the existence of multiple positive, multiple negative, and in particular, of multiple sign changing solutions depending on λ.

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