The existence of normalized solutions for a fractional Kirchhoff-type equation with doubly critical exponents

Multiple Solutions to a Non-Local Problem of Schrödinger–Kirchhoff Type in ℝN

“…(−∆) s p w(y) = 2 lim The study on elliptic problems with the non-local Kirchhoff term was initially introduced by Kirchhoff [7] to investigate an expansion of the classical D'Alembert's wave equation by taking the changes in the length of the strings during the vibrations into account. The variational problems of Kirchhoff type have a powerful background in various applications in physics and have been concentrically explored by many researchers in recent decades; as an illustration, see [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24] and the references therein. A detailed discussion about the physical implications based on the fractional Kirchhoff model was first proposed by the work of Fiscella and Valdinoci [25].…”