Nontrivial solution of a semilinear schrödinger equation

On a semilinear Schrödinger equation with critical Sobolev exponent

“…[1,3,5,9,11,13,16,17,18] and the references there. Equation (1.1) under conditions similar to (A1)-(A5) was discussed in [6], and our Theorem 1.1 is an extension of the main result there.…”

“…(i) See e.g. [11,18,19]. The proofs given there are for nonlinearities of subcritical growth but the argument remains unchanged in our case (the part showing J| ∂M ≤ 0 is in fact somewhat simpler here; observe only that (2…”

Infinitely many solutions for asymptotically linear periodic Hamiltonian elliptic systems

“…In what follows, we shall seek for the critical points of Φ under the assumptions on H. The functional Φ is strongly indefinite; such type of functionals have appeared extensively in the study of differential equations via critical point theory, see for example [19,26,27] and the references therein.…”

Solutions to a class of Schrödinger equations

“…We refer, e.g., to [10] for HartreeFock equations, [5] for Schrödinger operators of atoms and molecules, and [1], [3], [4], [6], [8], [12], [14] for the Schödinger operators with continuous (periodic etc.) potentials.…”