Existence of blow-up solutions for a non-linear equation with gradient term in RN

AbstractIn this paper we study the existence of positive large solutions for the equation Δpu+λ|∇u|p−1=ρ(x)f(u) in RN, where f is a non-negative non-decreasing function and ρ is a non-negative continuous function. We show under some hypotheses detailed below the existence of positive solutions which blow up at infinity

General Quasilinear Problems Involving P(X)-Laplacian with Robin Boundary Condition

This paper deals with the existence and multiplicity of solutions for a class of quasilinear problems involving p(x)-Laplace type equation, namely {−div(a(|∇u|p(x))|∇u|p(x)−2∇u)=λf(x,u)n⋅a(|∇u|p(x))|∇u|p(x)−2∇u+b(x)|u|p(x)−2u=g(x,u)inonΩ,∂Ω. Our technical approach is based on variational methods, especially, the mountain pass theorem and the symmetric mountain pass theorem

Existence of blow-up solutions for a non-linear equation with gradient term in RN

AbstractIn this paper we study the existence of positive large solutions for the equation Δpu+λ|∇u|p−1=ρ(x)f(u) in RN, where f is a non-negative non-decreasing function and ρ is a non-negative continuous function. We show under some hypotheses detailed below the existence of positive solutions which blow up at infinity

On a nonresonance condition between the first and the second eigenvalues for the p-Laplacian

We are concerned with the existence of solution for the Dirichlet problem −Δpu=f(x,u)+h(x) in Ω, u=0 on ∂Ω, when f(x,u) lies in some sense between the first and the second eigenvalues of the p-Laplacian Δp. Extensions to more general operators which are (p−1)-homogeneous at infinity are also considered

Existence and multiplicity results for nonlinear problems involving the p(x)-laplace operator

In this paper we study the following nonlinear boundary-value problem [formula] where Ω ⊂ RN is a bounded domain with smooth boundary [formula] is the outer unit normal derivative on [formula] are two real numbers such that [formula] is a continuous function on Ω with [formula] are continuous functions. Under appropriate assumptions on ƒ and g, we obtain the existence and multiplicity of solutions using the variational method. The positive solution of the problem is also considered

Strong unique continuation of eigenfunctions for p-Laplacian operator

We show the strong unique continuation property of the eigenfunctions for p-Laplacian operator in the case p<N

Existence of weak solutions for a quasilinear equation in RN

AbstractThis paper studies the p-Laplacian equation −Δpu+λVλ(x)|u|p−2u=f(x,u)inRN, where 1<p<N,λ≥1 and Vλ(x) is a nonnegative continuous function. Under some conditions on f(x,u) and Vλ(x), we prove the existence of nontrivial solutions for λ sufficiently large

Existence of solutions for a fourth order problem at resonance

abstract: In this work, we are interested at the existence of nontrivial solutions of two fourth order problems governed by the weighted p-biharmonic operator. The first is the following where λ 1 is the first eigenvalue for the eigenvalue problem ∆(ρ|∆u| p−2 ∆u) = λm(x)|u| p−2 u in Ω, u = ∆u = 0 on ∂Ω. In the seconde problem, we replace λ 1 by λ such that λ 1 &lt; λ &lt;λ, whereλ is given bellow