Related papers: Nodal solutions of weighted indefinite problems
We prove that a class of superlinear indefinite problems with homogeneous Neumann boundary conditions admits an arbitrarily high number of positive solutions, provided that the parameters of the problem are adequately chosen. The…
Second order nonlinear eigenvalue problems are considered for which the spectrum is an interval. The boundary conditions are of Robin and Dirichlet type. The shape and the number of solutions are discussed by means of a phase plane…
The aim of this article is to provide a simple and unified way to obtain the sharp upper bounds of nodal sets of eigenfunctions for different types of eigenvalue problems on real analytic domains. The examples include biharmonic Steklov…
In this paper, we study weakly nonlinear boundary value problems on infinite intervals. For such problems, we provide criteria for the existence of solutions as well as a qualitative description of the behavior of solutions depending on a…
We first study the linear eigenvalue problem for a planar Dirac system in the open half-line and describe the nodal properties of its solution by means of the rotation number. We then give a global bifurcation result for a planar nonlinear…
We consider the most general class of linear boundary-value problems for higher-order ordinary differential systems whose solutions and right-hand sides belong to the corresponding Sobolev spaces. For parameter-dependent problems from this…
This paper analyzes the structure of the set of positive solutions of a class of one-dimensional superlinear indefinite bvp's. It is a paradigm of how mathematical analysis aids the numerical study of a problem, whereas simultaneously its…
In this thesis, the numerical solution of three different classes of problems have been studied. Specifically, new techniques have been proposed and their theoretical analysis has been performed, accompanied by a wide set of numerical…
We investigate linear boundary value problems for first-order one-dimensional hyperbolic systems in a strip. We establish conditions for existence and uniqueness of bounded continuous solutions. For that we suppose that the non-diagonal…
By topological arguments, we prove new results on the existence, non-existence, localization and multiplicity of nontrivial solutions of a class of perturbed nonlinear integral equations. These type of integral equations arise, for example,…
In [5] the structure of the bifurcation diagrams of a class of superlinear indefinite problems with a symmetric weight was ascertained, showing that they consist of a primary branch and secondary loops bifurcating from it. In [4] it has…
In this article we are interested for the numerical study of nonlinear eigenvalue problems. We begin with a review of theoretical results obtained by functional analysis methods, especially for the Schrodinger pencils. Some recall are given…
We consider a non-polynomial cubic spline to develop the classes of methods for the numerical solution of singularly perturbed two-point boundary value problems. The proposed methods are second and fourth order accurate and applicable to…
This paper is to introduce a type of full multigrid method for the nonlinear eigenvalue problem. The main idea is to transform the solution of nonlinear eigenvalue problem into a series of solutions of the corresponding linear boundary…
In this article we study a class of generalised linear systems of difference equations with given boundary conditions and assume that the boundary value problem is non-consistent, i.e. it has infinite many or no solutions. We take into…
In this work, the Dirac-type integro di{\S}erential system with one classical boundary condition and another nonlocal integral boundary condition is considered. We obtain the asymptotic formulae for the solutions, eigenvalues and nodal…
Many problems in nonlinear analysis and optimization, among them variational inequalities and minimization of convex functions, can be reduced to finding zeros (namely, roots) of set-valued operators. Hence numerous algorithms have been…
The existence of numerical solutions to a fourth order singular boundary value problem arising in the theory of epitaxial growth is studied. An iterative numerical method is applied on a second order nonlinear singular boundary value…
This paper introduces a fast and numerically stable algorithm for the solution of fourth-order linear boundary value problems on an interval. This type of equation arises in a variety of settings in physics and signal processing. Our method…
This work investigates the application of the Newton's method for the numerical solution of a nonlinear boundary value problem formulated through an ordinary differential equation (ODE). Nonlinear ODEs arise in various mathematical modeling…