Existence of radial solutions for a p ( x ) p(x)p(x) -Laplacian Dirichlet problem

AbstractIn this paper, using variational methods, we prove the existence of at least one positive radial solution for the generalized $p(x)$ p ( x ) -Laplacian problem $$-\Delta _{p(x)} u + R(x) u^{p(x)-2}u=a (x) \vert u \vert ^{q(x)-2} u- b(x) \vert u \vert ^{r(x)-2} u$$ − Δ p ( x ) u + R ( x ) u p ( x ) − 2 u = a ( x ) | u | q ( x ) − 2 u − b ( x ) | u | r ( x ) − 2 u with Dirichlet boundary condition in the unit ball in $\mathbb{R}^{N}$ R N (for $N \geq 3$ N ≥ 3 ), where a, b, R are radial functions

Two Fixed-Point Theorems for Mappings Satisfying a General Contractive Condition of Integral Type in the Modular Space

First we prove existence of a fixed point for mappings defined on a complete modular space satisfying a general contractive inequality of integral type. Then we generalize fixed-point theorem for a quasicontraction mapping given by Khamsi (2008) and Ciric (1974)

A Periodic Solution of the Generalized Forced Liénard Equation

We consider the generalized forced Liénard equation as follows: (ϕp(x′))′+(f(x)+k(x)x′)x′+g(x)=p(t)+s. By applying Schauder's fixed point theorem, the existence of at least one periodic solution of this equation is proved

Some fixed point theorems for CC-class functions in bb-metric spaces

In this paper, via $C$-class functions, as a new class of functions, a fixed theorem in complete $b$-metric spaces is presented. Moreover, we study some results, which are direct consequences of the main results. In addition, as an application, the existence of a solution of an integral equation is given