Search

For a class of semilinear elliptic systems, the existence of a broader class of multibump solutions is established under considerably weaker conditions than in earlier works. The key tool is the use of variational methods. [ABSTRACT FROM AUTHOR]

This paper continues the recent study of an Allen-Cahn model PDE [1] by eliminating a strong spatial reversibility condition and by weakening certain nondegeneracy conditions on families of basic heteroclinic solutions, enabling us to obtain multibump solutions in a much more general setting. As in [1], novel minimization arguments play a key role in finding solutions. [ABSTRACT FROM AUTHOR]

This paper studies a Hamiltonian system possessing a double well potential for which the existence of multitransition heteroclinic and homoclinic solutions that are local minimizers of an associated functional is known. Under an additional mild non-degeneracy condition on the set of all homoclinic and heteroclinic solutions, the existence of further heteroclinic and homoclinic solutions that are of mountain pass type is established. A key tool for the existence arguments is a variant of the Mountain Pass Theorem that is of independent interest. [ABSTRACT FROM AUTHOR]