Existence and multiplicity of positive solutions for singular quasilinear problems

In this work we combine perturbation arguments and variational methods to study the existence and multiplicity of positive solutions for a class of singular p-Laplacian problems. In the first two theorems we prove the existence of solutions in the sense of distributions. By strengthening the hypotheses, in the third and last result, we establish the existence of two ordered positive weak solutions.     

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 symmetric positive solutions for a class of Sturm-Liouville-like boundary value problems

This paper deals with the existence of symmetric positive solutions for a class of singular Sturm-Liouville-like boundary value problems with a one-dimensional p-Laplacian operator. By using the fixed theorem of cone expansion and compression of norm type in a cone, the existence of positive solutions is established though nonlinear term contains the first derivative of unknown function.     

Multiplicity results for a Neumann problem involving the p-Laplacian

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

     

On the existence of positive radial solutions for a certain class of elliptic BVPs

The aim of this paper is to answer the question, when a certain BVP of elliptic type possesses positive radial solutions. We develop duality and variational principles for this problem. Our approach enables the approximation of solutions and gives a measure of a duality gap between primal and dual functional for minimizing sequences.     

Existence of positive solutions for some problems with nonlinear diffusion

In this paper we study the existence of positive solutions for problems of the type

where is the -Laplace operator and . If , such problems arise in population dynamics. Making use of different methods (sub- and super-solutions and a variational approach), we treat the cases , and , respectively. Also, some systems of equations are considered.

     

A note on a superlinear indefinite Neumann problem with multiple positive solutions

We prove the existence of three positive solutions for the Neumann problem associated to u^″+a(t)uγ+1=0, assuming that a(t) has two positive humps and is large enough. Actually, the result holds true for a more general class of superlinear nonlinearities.     

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 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.     

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.     

Multiplicity results for a Neumann problem withp-Laplacian and non-smooth potential

A multiplicity theorem for a non-smooth homogeneous Neumann problem withp-Laplacian is established through a locally Lipschitz continuous version of the Brézis-Nirenberg critical point result in presence of splitting. Some special cases are then pointed out.     

Multiplicity results for elliptic problems with variable exponent and nonhomogeneous Neumann conditions

Applying three critical point theorems, we prove the existence of at least three weak solutions for a class of differential equations with p(x)‐Laplacian and subject to small perturbations of nonhomogeneous Neumann conditions. Copyright © 2014 John Wiley & Sons, Ltd.     

A note on positive evanescent solutions for a certain class of elliptic problems

This paper is devoted to the existence and properties of solutions of the following class of nonlinear elliptic differential equations Δu(x)+f(x,u(x))+g(‖x‖)x⋅∇u(x)=0, x∈Rn, ‖x‖>R. We prove existence of positive solutions vanishing at positive infinity. Our approach is based on the subsolution and supersolution method. The nonlinearity f covers both sublinear and superlinear cases and does not necessarily satisfy f(x,0)≡0. The asymptotic behavior of solutions is also described.     

Some uniqueness results for a class of quasilinear elliptic eigenvalue problems

Existence and uniqueness results are obtained for positive radial solutions of a class of quasilinear elliptic equations in aN-ball or an annulus without monotone assumptions on the nonlinear termf. It is also proved that there is no non-radial positive solution. Supported by the Youth Foundations of National Education Commuttee and the Committee on Science and Technology of Henan Province     

The existence of countably many positive solutions for a system of nonlinear singular boundary value problems with the p-Laplacian operator

In this paper, we study the existence of countable many positive solutions for a class of nonlinear singular boundary value systems with p-Laplacian operator: