Panos K. Palamides

Nontrivial solutions of a nonlinear heat flow problem via Sperner’s Lemma

Abstract In this paper we investigate the existence of multiple nontrivial solutions of a nonlinear heat flow problem with nonlocal boundary conditions. Our approach relies on the properties of a vector field on the phase plane and utilizes Sperner’s Lemma, combined with the continuum property of the solutions funnel.

Positive solutions for higher-order Lidstone boundary value problems. A new approach via Sperner's Lemma

Abstract Consider the higher-order nonlinear scalar differential equation where associated to the Lidstone boundary conditions Existence of a solution of boundary value problems (BVP) (1),(2) such that are given, under superlinear or sublinear growth in f . Similarly, existence for the BVP (1)–(3), under the same assumptions, is proved such that We further prove analogous results for the case when , i.e., derivatives of the obtaining solution satisfy inverse inequalities. The approach is based on an analysis of the corresponding vector field on the face-plane and the well-known, from combinatorial analysis, Knaster-Kuratowski-Mazurkiewiczs principle or as it is known, Sperners Lemma.

Polynomial approximation to a non-local boundary value problem

In this paper, we construct a special class of polynomials which converge uniformly to the solution of a non-local boundary value problem (NBVP). The use of this special class is justified by the physics of the model which is described by this NBVP. This NBVP has been studied by Palamides et al. (2009) in [2], where the existence of solutions is established.

An existence theorem for a singular third-order boundary value problem on [0,+∞)

Abstract An existence result for a singular third-order boundary value problem is proved in this work. Here the nonlinearity is of the form f ( y ) = ( 1 − y ) λ g ( y ) , where λ > 0 and g ( y ) is continuous and positive on ( 0 , 1 ] , and the boundary conditions are y ( 0 ) = 0 , y ( + ∞ ) = 1 , y ′ ( + ∞ ) = y ″ ( + ∞ ) = 0 . The problem arises in the study of draining and coating flows.

Fourth-Order Four-Point Boundary Value Problem: A Solutions Funnel Approach

We investigate the existence of positive or a negative solution of several classes of fourpoint boundary-value problems for fourth-order ordinary differential equations. Although these