Homoclinic orbits for an unbounded superquadratic

Abstract

We consider the following nonperiodic diffusion systems where b ∈ C(ℝ × ℝN, ℝN, G ∈ C N (ℝ × ℝN × ℝ2m, ℝ) and Z: = (u, v): ℝ × ℝN → ℝm × ℝm. Suppose that the potential V is positive constant and G(t, x, z) is superquadratic in z as {pipe}z{pipe} → ∞. By applying a generalized linking theorem for strongly indefinite functionals, we obtain homoclinic solutions z satisfying z(t, x) → 0 as {pipe}(t, x){pipe} → ∞. © 2010 Birkhäuser/Springer Basel AG.