Existence of multiple solutions of Kirchhoff type equation with sign-changing potential

High energy solutions of modified quasilinear fourth-order elliptic equation

“…It was pointed out in [1][2][3][4] that (1.1) models several physical and biological systems where u describes a process which relies on the mean of itself such as the population density. For more mathematical and physical background on Kirchhoff-type problems, we refer the reader to [1,[5][6][7][8] and the references therein. It is well known that fourth-order elliptic equation has been widely studied since Lazer and Mckenna [9] first proposed to study periodic oscillations and traveling waves in a suspension bridge.…”

Fixed point theorems for cyclic contractive mappings via altering distance functions in metric-like spaces

“…Variational methods are used to prove the existence of solutions for differential equations [1][2][3][4][5][6][7][8][9]. However, fixed point methods are studied by many scholars [10][11][12][13] in different spaces.…”

Some new fuzzy fixed point theorems via distance functions with applications

“…Variational methods are used to prove the existence of solutions for differential equations [10,14,15,23,32,33,[35][36][37]. However, fixed point methods are studied by many scholars [12,13] in different spaces.…”