Submitted to Computers and Mathematics with Applications DOUBLE INTEGRAL CALCULUS OF VARIATIONS ON TIME SCALES

Abstract

ABSTRACT. We consider a version of the double integral calculus of variations on time scales, which includes as special cases the classical two-variable calculus of variations and the discrete two-variable calculus of variations. Necessary and sufficient conditions for a local extremum are established, among them an analogue of the Euler–Lagrange equation. AMS (MOS) Subject Classification. 39A0, 49K20. Keywords. Time scales; partial delta derivatives; double delta integrals; Euler–Lagrange equation