On a p-Kirchhoff equation via Fountain Theorem and Dual Fountain Theorem☆

By Duchao Liu. 2010

110 citations recorded by the source corpus.

Abstract In this paper, we show the existence of infinite solutions to the Kirchhoff type quasilinear elliptic equation [ M ( ∫ Ω ( ∣ ∇ u ∣ p + λ ( x ) ∣ u ∣ p ) d x ) ] p − 1 ( − Δ p u + λ ( x ) ∣ u ∣ p − 2 u ) = f ( x , u ) in a smooth bounded domain Ω ⊂ R N with nonlinear boundary condition ∣ ∇ u ∣ p − 2 ∂ u ∂ ν = η ∣ u ∣ p − 2 on ∂ Ω . The method we used here is based on “Fountain Theorem” and “Dual Fountain Theorem”.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/0a47337d44ae6ba973cfeac5773ce55a3fba1f0e

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In Applied Mathematics

In Computational Theory and Mathematics

In Control and Systems Engineering

Citations in the corpus

Multiplicity results for a class of $p(x)$-Kirchhoff type equations with combined nonlinearities (2012, background): “In recent years, elliptic problems involving p-Kirchhoff type operators have been studied in many papers, we refer to [2, 3, 4, 17, 18, 21, 22], in which the authors have used different methods to get the existence of solutions for (1.”
Soliton solutions to Kirchhoff type problems involving the critical growth in RN (2013, methodology): “In [18], the author showed the existence of infinite solutions to the p-Kirchhoff type quasilinear elliptic equation.”
Infinitely many solutions for a fractional Kirchhoff type problem via Fountain Theorem (2015, background): “Thus, our results and context in this section are more general than those of Liu in [23].”