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This paper explores a system of interacting `soft core' bosons in theGross-Pitaevskii mean-field approximation in a random Bernoulli potential.First, a condition for delocalization of the ground state wave function isproved which depends on the number of particles and interaction strength. Usingthis condition, asymptotics for ground state energy per particle are derived inthe large system limit for small values of the coupling constant. Our methodsdirectly describe the shape of the ground state in a given realization of therandom potential.

Ground State Energy of Mean-field Model of Interacting Bosons in Bernoulli Potential