On differential equations with exponential nonlinearities

Abstract

Two-point boundary value problems for the second order nonlinear ordinary differential equations, arising in the heat conductivity theory, are considered. Multiplicity and existence results are established. The properties of solutions are studied. Estimates of the number of solutions are obtained. A bifurcation analysis was made and the bifurcation curves were presented. The analytical technique together with the phase plane analysis is used to obtain the results.