Harmonic functions, defined as twice continuously differentiable functions satisfying Laplace’s equation, have long been a subject of intense study in both pure and applied mathematics.

A new definition of a guiding function for functional differential equations is given, which is sometimes better for applications than the known one by Mawhin. We then prove an existence result for ...

The closed-form solution of each of these general Cauchy-type problems is derived in terms of the function $ {\mathrm {\Phi }}_ {2}^ {\left (\mathrm {n}\right)}$ itself. Several special cases of the ...