  The existence and multiplicity of solutions for a class of non-local elliptic
boundary value problems with superlinear source functions are investigated in
this paper. Using variational methods, we examine the changes arise in the
solution behaviours as a result of the non-local effect. Comparisons are made
of the results here with those of the elliptic boundary value problem in the
absence of the non-local term under the same prescribed conditions to highlight
this effect of non-locality on the solution behaviours. Our results here
demonstrate that the complexity of the solution structures is significantly
increased in the presence of the non-local effect with the possibility ranging
from no permissible positive solution to three positive solutions and, contrary
to those obtained in the absence of the non-local term, the solution profiles
also vary depending on the superlinearity of the source functions.
