Qihu Zhang

Existence of solutions for p(x) -Laplacian dirichlet problem

This paper presents several sufficient conditions for the existence of solutions for the Dirichlet problem of p(x)-Laplacian {-div(|∇u|p(x)-2∇u) = f(x,u), x ∈ Ω, u = 0, x ∈ ∂Ω. Especially, an existence criterion for infinite many pairs of solutions for the problem is obtained. The discussion is based on the theory of the spaces Lp(x)(Ω) and W01, p(x)(Ω).

Solutions and nonnegative solutions for a weighted variable exponent impulsive integro-differential system with multi-point and integral mixed boundary value problems

This paper investigates the existence of solutions for a weighted p(t)-Laplacian impulsive integro-differential system with multi-point and integral mixed boundary value problems via Leray-Schauder’s degree; sufficient conditions for the existence of solutions are given. Moreover, we get the existence of nonnegative solutions.MSC:34B37.

Existence of solutions and nonnegative solutions for a class of p(t)-Laplacian differential systems with multipoint and integral boundary value conditions

This paper explores the existence of solutions for a class of p(t)-Laplacian differential systems with multipoint and integral boundary value conditions via Leray-Schauder’s degree. Moreover, the existence of nonnegative solutions is discussed.MSC:34B10.

Existence of Solutions for a Class of Variable Exponent Integrodifferential System Boundary Value Problems

This paper investigates the existence of solutions for a class of variable exponent integrodifferential system with multipoint and integral boundary value condition in half line. When the nonlinearity term 𝑓 satisfies sub-(𝑝−−1) growth condition or general growth condition, we give the existence of solutions and nonnegative solutions via Leray-Schauder degree at nonresonance, respectively. Moreover, the existence of solutions for the problem at resonance has been discussed.

Existence of solutions for weighted p(r)-Laplacian impulsive system mixed type boundary value problems

This paper investigates the existence of solutions for weighted p(r)-Laplacian impulsive system mixed type boundary value problems. The proof of our main result is based upon Gaines and Mawhins coincidence degree theory. Moreover, we obtain the existence of nonnegative solutions.

Existence and Asymptotic Behavior of Boundary Blow-Up Solutions for Weighted ()-Laplacian Equations with Exponential Nonlinearities

This paper investigates the following 𝑝(𝑥)-Laplacian equations with exponential nonlinearities: −Δ𝑝(𝑥)𝑢