Lipschitz continuity of solutions of a free boundary problem involving the p-Laplacian

We prove local interior and boundary Lipschitz continuity of solutions of a free boundary problem involving the p-Laplacian.     

Positive solution of three-point boundary value problem for the one-dimensional p-Laplacian with singularities

In the paper, we deal with positive solutions of the following nonlinear three-point singular boundary value problem with a p-Laplacian operator:

     

Multiple positive solutions to a three-point boundary value problem with p-Laplacian

Sufficient conditions are obtained that guarantee the existence of at least two positive solutions for the equation (g(u′(t)))′+a(t)f(u)=0 subject to boundary conditions, by a simple application of a new fixed-point theorem due to Avery and Henderson.     

Up-to boundary regularity for a singular perturbation problem of p-Laplacian type

In this paper we are interested in establishing up-to boundary uniform estimates for the one phase singular perturbation problem involving a nonlinear singular/degenerate elliptic operator. Our main result states: if Ω⊂Rn is a C1,α domain, for some 0<α<1 and uε verifies

     

Existence and iteration of positive solutions for a generalized right-focal boundary value problem with p-Laplacian operator

In the paper, we obtain the existence of positive solutions and establish a corresponding iterative scheme for the following third-order generalized right-focal boundary value problem with p-Laplacian operator:

     

p-Laplacian boundary value problems on exterior regions

This paper treats some variational principles for solutions of inhomogeneous p  -Laplacian boundary value problems on exterior regions U?R^N$U?{\mathbb{R}}^N$ with dimension N?3$N?3$. Existence-uniqueness results when p∈(1,N)$p\in (1,N)$ are provided in a space E^1,p(U)$E^{1,p}(U)$ of functions that contains W^1,p(U)$W^{1,p}(U)$. Functions in E^1,p(U)$E^{1,p}(U)$ are required to decay at infinity in a measure theoretic sense. Various properties of this space are derived, including results about equivalent norms, traces and an L^p$L^p$-imbedding theorem. Also an existence result for a general variational problem of this type is obtained.     

Multiplicity results for a Neumann problem involving the p-Laplacian

In this paper, we establish some multiplicity results for the following Neumann problem:

     

On a class of singular p-Laplacian boundary value problems

We prove the existence and nonexistence of positive solutions for the boundary value problem

     

Existence of positive solutions for the p-Laplacian with p-gradient term

In this paper, we study the existence of positive solutions for the p-Laplacian involving a p-gradient term. Due to the non-variational structure and the fact that the nonlinearity may be critical or supercritical, the variational method is no longer valid. Taking advantage of global C1,α estimates and the Liouville type theorems, we employ the blow-up argument to obtain the a priori estimates on solutions, and finally obtain the existence result based on the Krasnoselskii fixed point theorem.     

Bounds for the positive eigenvalues of the p-Laplacian with decaying potential

An upper bound is obtained for the positive eigenvalues of the p-Laplacian with decaying potential on [0,∞). The bound is expressed in terms of the potential and is shown to be the best possible of its kind.     

Nontrivial solutions for p-Laplacian systems

The paper deals with the existence and nonexistence of nontrivial nonnegative solutions for the sublinear quasilinear system

     

p-Laplacian problems with jumping nonlinearities

We consider the p-Laplacian boundary value problem

(1)     

Positive solutions of fourth-order four-point boundary value problems with p-Laplacian operator

In this paper, we consider the existence of positive solutions for the singular fourth-order p-Laplacian equation

     

Global attractors for p-Laplacian equation

The existence of a -global attractor is proved for the p-Laplacian equation ut−div(|∇u|^p−2∇u)+f(u)=g on a bounded domain Ω⊂Rn(n?3) with Dirichlet boundary condition, where p?2. The nonlinear term f is supposed to satisfy the polynomial growth condition of arbitrary order c₁q|u|−k?f(u)u?c₂q|u|+k and f^′(u)?−l, where q?2 is arbitrary. There is no other restriction on p and q. The asymptotic compactness of the corresponding semigroup is proved by using a new a priori estimate method, called asymptotic a priori estimate.     

Ordinary p-Laplacian systems with nonlinear boundary conditions

This paper is concerned with the existence of solutions for the boundary value problem

     

Uniqueness results for the one-dimensional p-Laplacian

This paper is concerned with positive solutions of the boundary value problem ^′(|y^′|^p−2y^′)+f(y)=0, y(−b)=0=y(b) where p>1, b is a positive parameter. Assume that f is continuous on (0,+∞), changes sign from nonpositive to positive, and f(y)/yp−1 is nondecreasing in the interval of f>0. The uniqueness results are proved using a time-mapping analysis.     

Resonance problems for the p-Laplacian systems

Two existence theorems of the solutions are obtained for the p-Laplacian systems at resonance under a Landesman-Lazer-type condition by critical point theory.     

Three positive solutions for the one-dimensional p-Laplacian

In this paper, nonlinear two point boundary value problems with p-Laplacian operators subject to Dirichlet boundary condition and nonlinear boundary conditions are studied. We show the existence of three positive solutions by the five functionals fixed point theorem.     

Landesman-Lazer type conditions for a system of p-Laplacian like operators

We study the existence of periodic solutions for a nonlinear second order system of ordinary differential equations of p-Laplacian type. Assuming suitable Nagumo and Landesman-Lazer type conditions we prove the existence of at least one solution applying topological degree methods. We extend a celebrated result by Nirenberg for resonant systems.