Some Remarks of the Antimaximum Principle and the Fucik Spectrum for the p-Laplacian

2002 ◽  
Author(s):  
A Dakkak
Keyword(s):  
Fučík Spectrum ◽  
Fučik Spectrum ◽  
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.

On the periodic Fučik spectrum and a superlinear Sturm–Liouville equation

1993 ◽  
Vol 123 (1) ◽  
pp. 95-107 ◽  
Author(s):  
Djairo G. Figueiredo ◽  
Bernhard Ruf
Keyword(s):  
Liouville Equation ◽  
Exponential Nonlinearity ◽  
Fučík Spectrum ◽  
Fučik Spectrum ◽  
Sturm Liouville ◽  
Fucik Spectrum

SynopsisIn the first part of the paper a variational characterisation of the periodic eigenvalues (the so-called Fučik spectrum) of a semilinear, positive homogeneous Sturm–Liouville equation is given. The proof relies on the S1-invariance of the equation.In the second part a nonlinear Sturm–Liouville equation with, typically, an exponential nonlinearity is considered. It is proved that under certain conditions this equation is solvable for arbitrary forcing terms. The proof uses a comparison of the minimax levels of the functional associated to this equation with suitable values in the Fučik spectrum.

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