scholarly journals Existence of solutions for fourth order elliptic equations of Kirchhoff type

2014 ◽  
Vol 409 (1) ◽  
pp. 140-146 ◽  
Author(s):  
Fanglei Wang ◽  
Mustafa Avci ◽  
Yukun An
Keyword(s):  
Fourth Order ◽  
Elliptic Equations ◽  
Existence Of Solutions ◽  
Kirchhoff Type ◽  
Fourth Order Elliptic Equations

scholarly journals Existence of Solutions for a Coupled System of Second and Fourth Order Elliptic Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-4 ◽  
Author(s):  
Fanglei Wang
Keyword(s):  
Fourth Order ◽  
Elliptic Equations ◽  
Existence Of Solutions ◽  
Coupled System ◽  
Monotone Sequence ◽  
Fourth Order Elliptic Equations ◽  
Quasilinearization Technique

The generalized quasilinearization technique is applied to obtain a monotone sequence of iterates converging uniformly and quadratically to a solution of a coupled system of second and fourth order elliptic equations.

Infinitely Many Solutions for Schrödinger–Kirchhoff-Type Fourth-Order Elliptic Equations

2017 ◽  
Vol 60 (4) ◽  
pp. 1003-1020 ◽  
Author(s):  
Hongxue Song ◽  
Caisheng Chen
Keyword(s):  
Fourth Order ◽  
Elliptic Equations ◽  
Mountain Pass Theorem ◽  
Infinitely Many Solutions ◽  
Biharmonic Operator ◽  
Kirchhoff Type ◽  
Symmetric Mountain Pass Theorem ◽  
Image Position ◽  
Fourth Order Elliptic Equations ◽  
Biharmonic Problems

AbstractThis paper deals with the class of Schrödinger–Kirchhoff-type biharmonic problemswhere Δ2 denotes the biharmonic operator, and f ∈ C(ℝN × ℝ, ℝ) satisfies the Ambrosetti–Rabinowitz-type conditions. Under appropriate assumptions on V and f, the existence of infinitely many solutions is proved by using the symmetric mountain pass theorem.

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