Principal Eigenvalues and Perturbation

1995 ◽  
pp. 39-55
Author(s):  
Wolfgang Arendt ◽  
Charles J. K. Batty
Keyword(s):  
Principal Eigenvalues

scholarly journals Principal eigenvalues for k-Hessian operators by maximum principle methods

2021 ◽  
Vol 3 (3) ◽  
pp. 1-37
Author(s):  
Isabeau Birindelli ◽  
◽  
Kevin R. Payne ◽  
◽  
◽  
...  
Keyword(s):  
Maximum Principle ◽  
Principal Eigenvalues

scholarly journals On a positive solution for $(p,q)$-Laplace equation with Nonlinear

2019 ◽  
Vol 38 (4) ◽  
pp. 219-133
Author(s):  
Abdellah Zerouali ◽  
Belhadj Karim ◽  
Omar Chakrone ◽  
Abdelmajid Boukhsas
Keyword(s):  
Eigenvalue Problem ◽  
Positive Solution ◽  
Laplace Equation ◽  
Existence Results ◽  
Indefinite Weight ◽  
Principal Eigenvalues ◽  
Steklov Eigenvalue ◽  
Indefinite Weights ◽  
Steklov Eigenvalue Problem

In the presentp aper, we study the existence and non-existence results of a positive solution for the Steklov eigenvalue problem driven by nonhomogeneous operator $(p,q)$-Laplacian with indefinite weights. We also prove that in the case where $\mu>0$ and with $1<q<p<\infty$ the results are completely different from those for the usua lSteklov eigenvalue problem involving the $p$-Laplacian with indefinite weight, which is retrieved when $\mu=0$. Precisely, we show that when $\mu>0$ there exists an interval of principal eigenvalues for our Steklov eigenvalue problem.

RESONANT GLUING BIFURCATIONS

2000 ◽  
Vol 10 (09) ◽  
pp. 2141-2160 ◽  
Author(s):  
ROBERT W. GHRIST
Keyword(s):  
Saddle Point ◽  
Parameter Space ◽  
Two Dimensional ◽  
Bifurcation Structure ◽  
Centre Manifold ◽  
Principal Eigenvalues ◽  
Homoclinic Connections ◽  
Homoclinic Bifurcations ◽  
Zero Entropy

We consider the codimension-three phenomenon of homoclinic bifurcations of flows containing a pair of orbits homoclinic to a saddle point whose principal eigenvalues are in resonance. We concentrate upon the simplest possible configuration, the so-called "figure-of-eight," and reduce the dynamics near the homoclinic connections to those on a two-dimensional locally invariant centre manifold. The ensuing resonant gluing bifurcations exhibit features of both gluing bifurcations and resonant homoclinic bifurcations. Under certain twist conditions, the bifurcation structure is extremely rich, although describing zero-entropy flows. The analysis carefully exploits the topology of the orbits, the centre manifold and the parameter space.

scholarly journals On Principal Eigenvalues ofp-Laplacian-like Operators

1996 ◽  
Vol 130 (1) ◽  
pp. 235-246 ◽  
Author(s):  
M. García-Huidobro ◽  
R. Manásevich ◽  
K. Schmitt
Keyword(s):  
Principal Eigenvalues

On Principal Eigenvalues for Indefinite Problems in Euclidean Space

1998 ◽  
Vol 192 (1) ◽  
pp. 205-223 ◽  
Author(s):  
Grigori Rozenblum ◽  
Michael Solomyak
Keyword(s):  
Euclidean Space ◽  
Principal Eigenvalues ◽  
Indefinite Problems
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