scholarly journals Sign-changing solutions for $p$-Laplacian equations with jumping nonlinearity and the Fučik spectrum

2016 ◽  
Vol 48 (1) ◽  
pp. 1 ◽  
Author(s):  
Ming Xiong ◽  
Ze-Heng Yang ◽  
Xiang-Qing Liu
Keyword(s):  
Fučík Spectrum ◽  
Fučik Spectrum ◽  
Jumping Nonlinearity ◽  
Sign Changing Solutions ◽  
Laplacian Equations ◽  
Fucik Spectrum

Fučík spectrum

2012 ◽  
pp. 67-106
Author(s):  
Kanishka Perera ◽  
Martin Schechter
Keyword(s):  
Fučík Spectrum ◽  
Fučik Spectrum ◽  
Fucik Spectrum

Complete structure of the Fučík spectrum of the p-Laplacian with integrable potentials on an interval

2016 ◽  
Vol 18 (06) ◽  
pp. 1550085 ◽  
Author(s):  
Wei Chen ◽  
Jifeng Chu ◽  
Ping Yan ◽  
Meirong Zhang
Keyword(s):  
Double Sequence ◽  
Neumann Boundary ◽  
Strong Continuity ◽  
Complete Structure ◽  
Spectral Curves ◽  
Fučík Spectrum ◽  
Fučik Spectrum ◽  
Differentiability Of Solutions ◽  
Asymptotic Lines ◽  
Fucik Spectrum

To characterize the complete structure of the Fučík spectrum of the [Formula: see text]-Laplacian on higher dimensional domains is a long-standing problem. In this paper, we study the [Formula: see text]-Laplacian with integrable potentials on an interval under the Dirichlet or the Neumann boundary conditions. Based on the strong continuity and continuous differentiability of solutions in potentials, we will give a comprehensive characterization of the corresponding Fučík spectra: each of them is composed of two trivial lines and a double-sequence of differentiable, strictly decreasing, hyperbolic-like curves; all asymptotic lines of these spectral curves are precisely described by using eigenvalues of the [Formula: see text]-Laplacian with potentials; and moreover, all these spectral curves have strong continuity in potentials, i.e. as potentials vary in the weak topology, these spectral curves are continuously dependent on potentials in a certain sense.

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