Positive solutions for a quasilinear elliptic equation of Kirchhoff type

By Claudianor Oliveira Alves, Francisco Júlio S. A. Corrêa, To Fu Ma. 2005

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This paper is concerned with the existence of positive solutions to the class of nonlocal boundary value problems of the type -M(@!"@W|@?u|^2dx)@Du=f(x,u),[email protected],u=0,[email protected][email protected], where @W is a smooth bounded domain of @?^N, M is a positive function, and f has subcritical growth.

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Citations in the corpus

Positive Solutions of Elliptic Kirchhoff Equations (2016, background): “Furthermore, if in (f3) we can take κ = λ1[1]M λ1[b]M∞ ,”
Study of a nonlinear Kirchhoff equation with non-homogeneous material (2014, methodology): “In [2] and [19] the Mountain Pass Theorem and a truncation argument is applied to prove the existence of a solution when f is subcritical (see also [9] for the critical case).”
Multiplicity of solutions for p ( x ) -polyharmonic elliptic Kirchhoff equations (2011, methodology): “The existence of positive solutions of non-degenerate Kirchhoff-type problems is treated in [7–9] for L = 1.”
On doubly nonlocal fractional elliptic equations (2015, result): “Hence, for any ν ∈ [1, 2), there exists cν > 0 such that ‖v‖Lν(IRn) ≤ cν‖v‖X0 , for every v ∈ X0.”
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, background): “In [2], it was pointed out that the problem (1.”