Nonlinear elliptic fourth order equations existence and multiplicity results

Existence and uniqueness results for a nonlinear differential equations of arbitrary order

This paper studies a fractional boundary value problem of nonlinear differential equations of arbitrary orders. New existence and uniqueness results are established using Banach contraction principle. Other existence results are obtained using Schaefer and Krasnoselskii fixed point theorems. In order to clarify our results, some illustrative examples are also presented.

Existence and multiplicity of solutions for a fourth-order elliptic equation

where Ω ⊂ R is a bounded smooth domain, f : Ω × R ® R and M : R ® R are continuous functions. The existence and multiplicity results for Equation (1) are considered in [1-3] by using variational methods and fixed point theorems in cones of ordered Banach space with space dimension is one. On the other hand, The four-order semilinear elliptic problem { 2u + c u = f (x, u), in , u = u = 0, on ∂ ,...

Existence and Comparison Results for Fully Nonlinear Degenerate Elliptic Equations without Zeroth-Order Term

New existence results for a coupled system of nonlinear differential equations of arbitrary order

This paper studies the existence of solutions for a coupled system of nonlinear fractional differential equations. New existence and uniqueness results are established using Banach fixed point theorem. Other existence results are obtained using Schaefer and Krasnoselskii fixed point theorems. Some illustrative examples are also presented.

Existence and multiplicity of solutions to boundary value problems for fourth-order impulsive differential equations

In this paper we study the existence and the multiplicity of solutions for an impulsive boundary value problem for fourth-order differential equations. The notions of classical and weak solutions are introduced. Then the existence of at least one and infinitely many nonzero solutions is proved, using the minimization, the mountain-pass, and Clarke's theorems.