scholarly journals Infinite number of solutions for some elliptic eigenvalue problems of Kirchhoff-type with non-homogeneous material

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Baoqiang Yan ◽  
Donal O’Regan ◽  
Ravi P. Agarwal
Keyword(s):  
Variational Method ◽  
Infinite Number ◽  
Eigenvalue Problems ◽  
Kirchhoff Equation ◽  
Homogeneous Material ◽  
Number Of Solutions ◽  
Reaction Term ◽  
Kirchhoff Type ◽  
Nonlinear Reaction ◽  
Elliptic Eigenvalue Problems

AbstractIn this paper, using variational method, we study the existence of an infinite number of solutions (some are positive, some are negative, and others are sign-changing) for a non-homogeneous elliptic Kirchhoff equation with a nonlinear reaction term.

On a Class of Semilinear Elliptic Eigenvalue Problems in ℝ2

2016 ◽  
Vol 60 (1) ◽  
pp. 107-126 ◽  
Author(s):  
Marcelo F. Furtado ◽  
Everaldo S. Medeiros ◽  
Uberlandio B. Severo
Keyword(s):  
Eigenvalue Problems ◽  
Weighted Sobolev Space ◽  
Positive Parameter ◽  
Number Of Solutions ◽  
Rapid Decay ◽  
Semilinear Elliptic ◽  
Exponential Critical Growth ◽  
Image Position ◽  
Elliptic Eigenvalue Problems ◽  
Semilinear Problem

AbstractWe consider the semilinear problemwhere λ is a positive parameter and f has exponential critical growth. We first establish the existence of a non-zero weak solution. Then, by assuming that f is odd, we prove that the number of solutions increases when the parameter λ becomes large. In the proofs we apply variational methods in a suitable weighted Sobolev space consisting of functions with rapid decay at infinity.

Free-surface flows with two stagnation points

1996 ◽  
Vol 324 ◽  
pp. 393-406 ◽  
Author(s):  
J.-M. Vanden-Broeck ◽  
F. Dias
Keyword(s):  
Free Surface ◽  
Infinite Number ◽  
Wave Breaking ◽  
Free Surface Flows ◽  
Number Of Solutions ◽  
Surface Flows ◽  
Stagnation Points ◽  
Surface Profiles ◽  
Countably Infinite

Symmetric suction flows are computed. The flows are free-surface flows with two stagnation points. The configuration is related to the modelling of wave breaking at the bow of a ship. It is shown that there is a countably infinite number of solutions and that the free-surface profiles are characterized by waves.

scholarly journals Asymptotic behavior for a viscoelastic Kirchhoff equation with distributed delay and Balakrishnan–Taylor damping

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Abdelbaki Choucha ◽  
Salah Boulaaras
Keyword(s):  
Asymptotic Behavior ◽  
Decay Rate ◽  
Energy Method ◽  
Distributed Delay ◽  
Type Equation ◽  
General Decay ◽  
Kirchhoff Equation ◽  
General Decay Rate ◽  
Kirchhoff Type ◽  
Nonlinear Viscoelastic

AbstractA nonlinear viscoelastic Kirchhoff-type equation with Balakrishnan–Taylor damping and distributed delay is studied. By the energy method we establish the general decay rate under suitable hypothesis.

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