scholarly journals INFINITELY MANY SOLUTIONS FOR A CLASS OF MODIFIED NONLINEAR FOURTH-ORDER ELLIPTIC EQUATIONS ON ℝN

2017 ◽  
Vol 54 (3) ◽  
pp. 895-909 ◽  
Author(s):  
Guofeng Che ◽  
Haibo Chen
Keyword(s):  
Fourth Order ◽  
Elliptic Equations ◽  
Infinitely Many Solutions ◽  
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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