On an elliptic equation of p-Kirchhoff type via variational methods

By Francisco Júlio, S. Correa, Giovany M. Figueiredo. Bulletin of the Australian Mathematical Society, 2006

261 citations recorded by the source corpus.

This paper is concerned with the existence of positive solutions to the class of nonlocal boundary value problems of the p-Kirchhoff type and where Ω is a bounded smooth domain of ℝN, 1 < p < N, s ≥ p* = (pN)/(N – p) and M and f are continuous functions.

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

View Paper: https://www.semanticscholar.org/paper/0470bb5cdfc7805c5c5b854063f0bca1581d070c

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In Applied Mathematics

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In Control and Systems Engineering

Citations in the corpus

Global Nonexistence for Nonlinear Kirchhoff Systems (2010, background): “In recent years, the study of p-Kirchhoff equations involving the quasilinear homogeneous p-Laplace operator, based on the theory of standard Sobolev spaces W 1,p 0 ( ), has been widely studied, see, for example, [6,25], while for wave equations [7], and for the elliptic case [5,8].”
Existence of solutions for fourth order elliptic equations of Kirchhoff type (2014, unknown): “For example, in [1, 5, 6, 15], the authors studied the existence of positive solutions of second order non-degenerate Kirchhofftype problems; in [4], F.”
Multiple solutions for nonhomogeneous Schrödinger–Kirchhoff type equations involving the fractional p-Laplacian in RN\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setl (2015, methodology): “For example, we refer to [18] for nondegenerate Kirchhoff type problems and [15,17] for degenerate Kirchhoff type problems.”
Multiplicity of solutions for p ( x ) -polyharmonic elliptic Kirchhoff equations (2011, background): “• ForL = 1, ∆p becomes the p–Laplacian ∆p; in this case in [6] is proved the existence of positive solutions for non– degenerate Kirchhoff functions M .”
Multiplicity results for the non-homogeneous fractional p-Kirchhoff equations with concave–convex nonlinearities (2015, background): “6) has received a lot of attention, and some interesting results can be found in, for example, [32] for the non-degenerate case and [33] for the degenerate case, also in [34] for the time case.”
Infinitely many solutions for a fractional Kirchhoff type problem via Fountain Theorem (2015, methodology): “For example, we refer to [13] for non-degenerate Kirchhoff type problems and [12,11] for degenerate Kirchhoff type problems.”