Positive Solutions for a Higher-Order m-Point Boundary Value Problem

Abstract

We study the existence of positive solutions for a higher-order nonlinear differential system subject to some m-point boundary conditions. As applications of the main results, we present two existence theorems for the positive solutions of a higher-order nonlinear differential equation with boundary conditions of the same form as those for the studied system. (2010). Primary 34B10; Secondary 34B18. Mathematics Subject Classification

Existence and multiplicity for positive solutions of a system of higher-order multi-point boundary value problems

“…Some particular cases of the above problems have been studied in [6][7][8][9]12,13,15]. In recent years, the multi-point boundary value problems for secondorder or higher-order differential or difference equations/systems have been investigated by many authors, by using different methods such as fixed point theorems in cones, the Leray-Schauder continuation theorem and its nonlinear alternatives and the coincidence degree theory.…”

Positive solutions for singular systems of multi‐point boundary value problems

“…Some discrete versions of the preceding problems were studied in [14][15][16][17][18][19][20]. For the case of higher-order nonlinear differential systems subject to multi-point boundary conditions, we would like to mention the papers [21][22][23][24][25].…”

Existence and Nonexistence of Positive Solutions for a System of Higher-Order Di erential Equations with Integral Boundary Conditions

“…Problems with integral boundary conditions arise in thermal conduction problems, semiconductor problems and hydrodynamic problems. In the last decades, many authors investigated differential equations or systems of differential equations with integral boundary conditions, for which they prove the existence, multiplicity and nonexistence of positive solutions by using various methods, such as fixed point theorems in cones, the LeraySchauder continuation theorem, nonlinear alternatives of Leray-Schauder type, fixed point index theory and coincidence degree theory (see, for example, [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15]). …”