On the existence of multiple positive entire solutions for a class of quasilinear elliptic equations

Our goal is to establish the theorems of existence and multiple of positive entire solutions for a class quasilinear elliptic equations in ℝN with the Schauder-Tychonoff fixed point theorem as the principal tool. In many articles, the theorems of existence and multiple of positive entire solutions for a class semilinear elliptic equations are established. The results of the semilinear equations are extended to the quasilinear ones and the results of semilinear equations are developed

Analytic Solution of a Class of Fractional Differential Equations

We consider the analytic solution of a class of fractional differential equations with variable coefficients by operatorial methods. We obtain three theorems which extend the Garra’s results to the general case

Global Existence and Blow-Up Solutions and Blow-Up Estimates for Some Evolution Systems with p

This paper deals with p-Laplacian systems ut−div(|∇u|p−2∇u)=∫Ωvα(x, t)dx, x∈Ω, t>0, vt−div(|∇v|q−2∇v)=∫Ωuβ(x,t)dx, x∈Ω, t>0, with null Dirichlet boundary conditions in a smooth bounded domain Ω⊂ℝN, where p,q≥2, α,β≥1. We first get the nonexistence result for related elliptic systems of nonincreasing positive solutions. Secondly by using this nonexistence result, blow up estimates for above p-Laplacian systems with the homogeneous Dirichlet boundary value conditions are obtained under Ω=BR={x∈ℝN:|x|0). Then under appropriate hypotheses, we establish local theory of the solutions and obtain that the solutions either exist globally or blow up in finite time

Positive Solutions for a Class of Quasilinear Elliptic Equations with a Dirichlet Problem

In this paper, we study the following problem -Δ_p u = h(x)u^q + f(u), u∈W_0^{1,p}(Ω), u > 0 in Ω, where Ω is a bounded smooth domain in R^N (N ≥ 3), 0 < q < 1. By using Mountain Pass Theorem, we prove that there exists at least two positive solutions under suitable assumptions on the nonlinearity. Key Words: Quasilinear elliptic equation; Positive solution; Dirichlet problem; Mountain Pass Theore

Nonexistence of positive solutions to a quasilinear elliptic system and blow-up estimates for a non-Newtonian filtration system

AbstractThe prior estimate and decay property of positive solutions are derived for a system of quasilinear elliptic differential equations first. Then the result of nonexistence for a differential equation system of radially nonincreasing positive solutions is implied. By using this nonexistence result, blow-up estimates for a class of quasilinear reaction-diffusion systems (non-Newtonian filtration systems) are established to extend the result of semilinear reaction-diffusion (Fujita type) systems

Nonexistence of positive solutions to a quasilinear elliptic system and blow-up estimates for a quasilinear reaction–diffusion system

AbstractThe prior estimate and decay property of positive solutions are derived for a system of quasilinear elliptic differential equations first. Then, the nonexistence result for radially nonincreasing positive solutions of the system is implied. By using this nonexistence result, blow-up estimates for a class of quasilinear reaction–diffusion systems (non-Newtonian filtration systems) are established to extend the result for semilinear reaction–diffusion systems (Fujita type)

ON POSITIVE SOLUTION FOR A CLASS OF QUASILINEAR ELLIPTIC SYSTEMS WITH SIGN-CHANGING WEIGHTS

In this paper, we consider the problem for the existence of positive solutions of quasilinear elliptic system where the λ &gt; 0 is a parameter, Ω is a bounded domain in R N (N &gt; 1) with smooth boundary ∂ Ω , and the Δ p z = div(|∇z| p−2 ∇z) is the p -Laplacian operator. Here a(x) and b(x) are C 1 sign-changing functions that maybe are negative near the boundary. Using the method of sub-super solutions and comparison principle, which studied the existence of positive solutions for quasilinear elliptic system. The main results of the present paper are new and extend the previously known results

An Experimental Study on Shear Performance of Adhesive Interface between Steel Plates and CFRP

CFRP (Carbon Fiber Reinforced Polymer) are widely used in steel structural reinforcement. For steel structures strengthened with CFRP, except the cases the structures have defects before strengthening, the adhesive interface is the weakest part and CFRP debonding is the most common failure mode. In order to investigate the failure mechanism of CFRP strengthened steel structures, this paper presents an experimental study on shear performance of adhesive interface between steel plate and CFRP by twin shear model. Six steel plates strengthened with CFRP are divided into two groups, one has no damage, another has a gap at the mid. The specimens are tested under tensile loadings. The study results show that, the plates with a gap failed for CFRPs debonding, the cracking loading and breaking loading are 14.85kN, and 17.88kN respectively; the strain-loading curves had long linear stages, two strains decrease and other strains of another side increased rapidly at the cracking loading, then they both rose until the plates failed