Existence of a positive solution for a Kirchhoff problem type with critical growth via truncation argument

Multiple positive solutions for Kirchhoff type of problems with singularity and critical exponents

“…There are some recent papers on the Kirchhoff type of problem involving critical exponent, see [21,1,7,11,8]. In particular, in [1], Alves, Corrêa, and Figueiredo have studied the existence of solutions for equations…”

Study of a nonlinear Kirchhoff equation with non-homogeneous material

“…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). In [8] the Mountain Pass Theorem and the Ekeland's Principle were used to show the existence of multiple non-trivial solutions of (1.3) with a concave nonlinearity.…”

Signed and sign-changing solutions for a Kirchhoff-type equation in bounded domains

“…In the last ten years, by classical variational method, there are many interesting results about the existence and nonexistence of solutions, sign-changing solutions, ground state solutions, the existence of positive solutions and positive ground states, least energy nodal solutions, multiplicity of solutions, semiclassical limit and concentrations of solution to Kirchhoff type problems, see e.g. [1,4,[6][7][8][9][10][11]13,14,16,[19][20][21] and the references therein.…”

“…We would like to point out that it is the work [6] that gives us the primal idea for dealing with problem (P λ ) with more general nonlinearity which may not have 4-superlinear growth. That paper concerns the following problem:…”