A nondegeneracy condition for a semilinear elliptic system and the existence of 1- bump solutions (Q2335354)

Some general considerations are provided in order to describe the situation for what concerns the existence of multi-bump solutions for semilinear elliptic systems on the whole space and homoclinic solutions to Hamiltonian systems. Several variational methods are combined, starting with Mountain Pass Theorem arguments for 1-bump solutions. Several non-degeneracy conditions on the systems are considered in different works. Under the conditions (ND3) a first result, Theorem 1.1, in this direction is proved here. The authors claim that the constructions of multi-bump solutions along this line of work is lengthly and will be developed elsewhere.