Existence and multiple solutions for a nonlinear system with a parameter

In this paper, the critical point theory and the Morse theory are employed to discuss the system of nonlinear equations of the form Au=λf(u)$Au=\lambda f\left(u\right)$, where the matrix A$A$ is not necessarily positive definite. Some existence and multiple solutions are obtained.     

Transition-layer solutions of quasilinear elliptic boundary blow-up problems and dirichlet problems

We study profiles of positive solutions for quasilinear elliptic boundary blow-up problems and Dirichlet problems with the same equation:

Nontrivial solutions for semilinear dirichlet forms via morse theory

Using variational methods and Morse theory, we obtain some existence results of multiple solutions for certain semilinear problems associated with general Dirichlet forms.     

Existence of solutions of nonlocal perturbations of dirichlet discrete nonlinear problems

This paper is devoted to the study of second order nonlinear difference equations. A Nonlocal Perturbation of a Dirichlet Boundary Value Problem is considered. An exhaustive study of the related Green's function to the linear part is done. The exact expression of the function is given, moreover the range of parameter for which it has constant sign is obtained. Using this, some existence results for the nonlinear problem are deduced from monotone iterative techniques, the classical Krasnoselski fixed point theorem or by application of recent fixed point theorems that combine both theories.     

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.

     

Existence of solutions for a class of third-order nonlinear boundary value problems

In this paper, we are concerned with the following third-order ordinary differential equation:

     

Approximate variational-iterative solutions for a class of nonlinear operator problems

A general theory for the approximate solution of nonlinear operator equations where the solution lies in some real or complex Hilbert space is developed. It is shown that the techniques can be applied to a variety of problems taken from the theories of plasma physics, colloid theory, and the theory of current flow in nerve membranes.     

Positive solutions for nonlinear singular boundary value problems

Some sufficient conditions for the existence of positive solutions to Dirichlet boundary value problems of a class of nonlinear second order differential equations are given.     

Resonant semilinear problems with nonlinear term depending on the derivative

We study the existence of solution for a boundary value problem at resonance where the nonlinearity depends only on the derivative. In a sense, we can say that the problem considered is strongly resonant. Our proofs make use of the Lyapunov-Schmidt reduction; in so doing, we are led with the asymptotic estimate of the corresponding bifurcation equation.     

High-order nonlinear boundary value problems admitting multiple exact solutions with application to the fluid flow over a sheet

We frame a hierarchy of nonlinear boundary value problems which are shown to admit exponentially decaying exact solutions. We are able to convert the question of the existence and uniqueness of a particular solution to this nonlinear boundary value problem into a question of whether a certain polynomial has positive real roots. Furthermore, if such a polynomial has at least two distinct positive roots, then the nonlinear boundary value problem will have multiple solutions. In certain special cases, these boundary value problems arise in the self-similar solutions for the flow of certain fluids over stretching or shrinking sheets; examples given include the flow of first and second grade fluids over such surfaces.     

On a class of semipositone discrete boundary value problems

In this paper, we deal with a class of semipositone discrete boundary value problems via critical point theory developed by Chang, and obtain nonexistence and multiplicity results on sublinear nonlinearities and an existence result on superlinear nonlinearities, respectively.     

Infinitely many solutions for a class of discrete non-linear boundary value problems

The existence of infinitely many solutions for a discrete non-linear Dirichlet problem involving the p-Laplacian, under appropriate oscillating behaviours of the non-linear term, is established. The approach is based on the critical point theory.     

Multiplicity results for a class of boundary value problems with impulsive effects

In this paper we study a class of boundary value problems with impulsive effects. Under some natural assumptions, by using Morse theory in combination with the minimax arguments, we establish some new results on the existence of multiple nontrivial solutions for the problems. Recent results from the literature are improved and extended.