Multiplicity of positive solutions to a p-Laplacian equation involving critical nonlinearity

In this paper we deal with multiplicity of positive solutions to the p-Laplacian equation of the type

     

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structure and the fact that the nonlinearity may be critical or supercritical, the variational method is no longer valid.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.     

On the existence of periodic solutions to p-Laplacian Rayleigh differential equation with a delay

In this paper, the authors study the existence of periodic solutions to a p-Laplacian Rayleigh differential equation with a delay as follows:

(φp(y^′(t))^)′+f(y^′(t))+g(y(t−τ(t)))=e(t),     

Multiple positive solutions of the one-dimensional p-Laplacian

In this work we investigate the existence of positive solutions of the p-Laplacian, using the quadrature method. We prove the existence of multiple solutions of the one-dimensional p-Laplacian for α?0, and determine their exact number for α=0.     

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.     

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.     

Existence of multiple positive solutions for one-dimensional p-Laplacian

In this paper we consider the multipoint boundary value problem for one-dimensional p-Laplacian

     

Periodic solutions for the 1-dimensional p-Laplacian equation

Existence of infinitely many periodic solutions for the 1-dimensional p-Laplacian equation

     

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.     

On the existence of periodic solutions for a class of p-Laplacian system

By using generalized Borsuk theorem in coincidence degree theory, some criteria to guarantee the existence of ω-periodic solutions for a class of p-Laplacian system are derived.     

Periodic solutions of the evolutionary p-Laplacian with nonlinear sources

This paper is concerned with the evolutionary p-Laplacian with nonlinear and periodic sources. We will give a rather complete characterization, in terms of the parameter p and the exponent q of the source, of whether or not the positive periodic solutions exist.     

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.     

Nontrivial solutions for p-Laplacian systems

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

     

Existence and multiplicity of positive solutions for the p-Laplacian with nonlocal coefficient

We consider the Dirichlet problem with nonlocal coefficient given by in a bounded, smooth domain Ω⊂Rn (n?2), where Δp is the p-Laplacian, w is a weight function and the nonlinearity f(u) satisfies certain local bounds. In contrast with the hypotheses usually made, no asymptotic behavior is assumed on f. We assume that the nonlocal coefficient (q?1) is defined by a continuous and nondecreasing function satisfying a(t)>0 for t>0 and a(0)?0. A positive solution is obtained by applying the Schauder Fixed Point Theorem. The case a(t)=tγ/q (0<γ<p−1) will be considered as an example where asymptotic conditions on the nonlinearity provide the existence of a sequence of positive solutions for the problem with arbitrarily large sup norm.     

Existence of three positive solutions for boundary value problems with p-Laplacian

By using fixed point theorem, we study the following equation g(u^′′(t))+a(t)f(u)=0 subject to boundary conditions, where g(v)=|v|^p−2v with p>1; the existence of at least three positive solutions is proved.     

Multiple solutions to p-Laplacian problems with concave nonlinearities

In this paper we study the p-Laplacian type elliptic problems with concave nonlinearities. Using some asymptotic behavior of f at zero and infinity, three nontrivial solutions are established.     

Existence of triple positive solutions to a class of p-Laplacian boundary value problems

By using Leggett-Williams' fixed-point theorem, a class of p-Laplacian boundary value problem is studied. Sufficient conditions for the existence of triple positive solutions are established.     

Periodic solutions of second-order differential inclusions systems with p-Laplacian

Some existence results are obtained for periodic solutions of nonautonomous second-order differential inclusions systems with p-Laplacian.     

Multiple positive solutions for multipoint boundary value problems with one-dimensional p-Laplacian

In this paper we consider the multiplicity of positive solutions for the one-dimensional p-Laplacian differential equation (?p^′(u^′))+q(t)f(t,u,u^′)=0, t∈(0,1), subject to some boundary conditions. By means of a fixed point theorem due to Avery and Peterson, we provide sufficient conditions for the existence of multiple positive solutions to some multipoint boundary value problems.     

Multiple solutions for a system of equations with p-Laplacian

In the paper, by using of the Limit Index, we prove a theorem applying to get multiple critical values of some strongly indefinite nonsmooth functionals, and then we apply it to a system of equations involving the p-Laplacian.