Existence and Multiplicity Results for Kirchhoff Problems

Existence and Uniqueness of Positive Solution for p-Laplacian Kirchhoff-Schrödinger-Type Equation

“…For a more complex situation, we refer the reader to [14]. The related studies on the elliptic equations also can be found in [15][16][17][18][19][20][21][22][23][24][25][26].…”

Strong Solutions and Global Attractors for Kirchhoff Type Equation

“…In particular, the function represents the displacement from equilibrium, is the velocity, and the term ( ) − may correspond to a (nonlinear) elastic force. For more details on the model of Kirchhoff, one can refer to [1][2][3] and the reference therein.…”

“…Let ( , ) = ( ) and(2) and(3) hold, (0) = 0. Then : ( )× 1 → ) and ( ) : ( ) → are continuous compact.Since ( ) × 1 → 1 × 2 ,from Theorem 5 and [4], we can immediately obtain the following result.…”

“…Suppose that ∈ 2 (Ω), ∈ 3 ( , ), (0) = 0, and(2) and(3) hold. Then the solution semigroup { ( )} ≥0 of problem (1) has global attractor A in 2 ; it attracts all bounded subset of 2 in the norm of 2 .…”

New Fixed Point Theorems and Application of Mixed Monotone Mappings in Partially Ordered Metric Spaces

“…Recently, there have been a lot of generalizations of the Banach contraction-mapping principle in the literature (see [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28]). Investigation of the existence of fixed points for single-valued mappings in partially ordered metric spaces was initially considered by Ran and Reurings in [29] who proved the existence of a unique fixed point.…”