scholarly journals Existence and multiplicity results for some weakly nonlinear elliptic problems at resonance

1983 ◽  
Vol 108 (3) ◽  
pp. 272-284
Author(s):  
Pavel Drábek
Keyword(s):  
Elliptic Problems ◽  
Nonlinear Elliptic Problems ◽  
Multiplicity Results ◽  
Weakly Nonlinear ◽  
Nonlinear Elliptic ◽  
Existence And Multiplicity ◽  
At Resonance

Existence and Multiplicity of Solutions for Nonlinear Elliptic Problems with the Fractional Laplacian

2015 ◽  
Vol 18 (1) ◽  
Author(s):  
Qing-Mei Zhou ◽  
Ke-Qi Wang
Keyword(s):  
Eigenvalue Problem ◽  
Critical Points ◽  
Fractional Laplacian ◽  
Nonlinear Eigenvalue Problem ◽  
Elliptic Problems ◽  
Nonlinear Elliptic Problems ◽  
Three Solutions ◽  
Multiplicity Of Solutions ◽  
Nonlinear Elliptic ◽  
Existence And Multiplicity

AbstractIn this paper we consider a nonlinear eigenvalue problem driven by the fractional Laplacian. By applying a version of the three-critical-points theorem we obtain the existence of three solutions of the problem in

Remarks on Nonlinear Elliptic Problems on Long Domains

2005 ◽  
Vol 5 (2) ◽  
Author(s):  
E.N. Dancer
Keyword(s):  
Elliptic Equations ◽  
Turning Point ◽  
Elliptic Problems ◽  
Nonlinear Elliptic Equations ◽  
Homoclinic Solutions ◽  
Local Uniqueness ◽  
Nonlinear Elliptic Problems ◽  
Weakly Nonlinear ◽  
Nonlinear Elliptic ◽  
Domain Length

AbstractIn this paper, we discuss the behaviour of solutions near a turning point for weakly nonlinear elliptic equations on long domains. We are looking for results independent of the domain length. In the process we obtain some local uniqueness and non-degeneracy results for homoclinic solutions on infinite strips.

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