Existence of Solutions for a Quasilinear System with Gradient Terms

In this paper, it is considered the existence of solutions for a quasilinear system involving the p-Laplacian operator and gradient terms. The approach is based on sub-supersolution arguments and the Schauder's Fixed Point Theorem. The results in this paper allow to consider several growth conditions in the gradient and complete some recent contributions.

Solutions of the Two-Wave Interactions in Quadratic Nonlinear Media

In this paper, we propose a reliable treatment for studying the two-wave (symbiotic) solitons of interactions in nonlinear quadratic media. We investigate the Schauder’s fixed point theorem for proving the existence theorem. Additionally, the uniqueness solution for this system is proved. Also, a highly accurate approximate solution is presented via an iteration algorithm.

On positive weak solutions for a class of weighted (p(.), q(.))−Laplacian systems

In this paper, we study the existence of positive weak solutions for a quasilinear elliptic system involving weighted (p(.), q(.))−Laplacian operators. The approach is based on sub-supersolutions method and on Schauder’s fixed point theorem.

Existence and Attractivity Results for Coupled Systems of Nonlinear Volterra–Stieltjes Multidelay Fractional Partial Integral Equations

We are concerned with some existence and attractivity results of a coupled fractional Riemann–Liouville–Volterra–Stieltjes multidelay partial integral system. We prove the existence of solutions using Schauder’s fixed point theorem; then we show that the solutions are uniformly globally attractive.

Schauder’s fixed-point theorem in approximate controllability problems

The main objective of this article is to present the state of the art concerning approximate controllability of dynamic systems in infinite-dimensional spaces. The presented investigation focuses on obtaining sufficient conditions for approximate controllability of various types of dynamic systems using Schauder’s fixed-point theorem. We describe the results of approximate controllability for nonlinear impulsive neutral fuzzy stochastic differential equations with nonlocal conditions, impulsive neutral functional evolution integro-differential systems, stochastic impulsive systems with control-dependent coefficients, nonlinear impulsive differential systems, and evolution systems with nonlocal conditions and semilinear evolution equation.

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.