An elliptic equation with spike solutions concentrating at local minima of the Laplacian of the potential.
Interfering solutions of a nonhomogeneous Hamiltonian system.
Heteroclinic solutions to an asymptotically autonomous second-order equation.
Existence of solutions to a Hamiltonian system without convexity condition on the nonlinearity.
Scattered homoclinics to a class of time-recurrent Hamiltonian systems
A second-order Hamiltonian system with time recurrence is studied. The recurrence condition is weaker than almost periodicity. The existence is proven of an infinite family of solutions homoclinic to zero whose support is spread out over the real line.
An elliptic equation with no monotonicity condition on the nonlinearity
An elliptic PDE is studied which is a perturbation of an autonomous equation. The existence of a nontrivial solution is proven variational methods. The domain of the equation is unbounded, which imposes a lack of compactness on the variational problem. In addition, a popular monotonicity condition on the nonlinearity is not assumed. In an earlier paper with this assumption, a solution was obtained using a simple application of topological (Brouwer) degree. Here, a more subtle degree...
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