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Existence of nontrivial weak solutions for p-biharmonic Kirchhoff-type equations
- Existence of nontrivial weak solutions for p-biharmonic Kirchhoff-type equations
- Bae J.-H.; Kim J.-M.; Lee J.; Park K.
- Ewha Authors
- Issue Date
- Journal Title
- Boundary Value Problems
- Boundary Value Problems vol. 2019, no. 1
- Kirchhoff type; p-biharmonic; Variational method
- Springer International Publishing
- Document Type
- We are concerned with the following p-biharmonic equations: Δp2u+M(∫RNΦ0(x,∇u)dx)div(φ(x,∇u))+V(x)
p−2u=λf(x,u)in RN, where 2 < 2 p< N, Δp2u=Δ(
p−2Δu), the function φ(x, v) is of type
p − 2v, φ(x,v)=ddvΦ0(x,v), the potential function V: RN→ (0 , ∞ ) is continuous, and f: RN× R→ R satisfies the Carathéodory condition. We study the existence of weak solutions for the problem above via mountain pass and fountain theorems. © 2019, The Author(s).
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