In this paper we study the Schrödinger equation of the form (P λ) -Δu + a(x)u = λb(x) f (u), x ⊂ ℝN, u ⊂ H1 (ℝN), where λ > 0 is a parameter, a and b are positive potentials, while the nonlinear term f : ℝ → ℝ is sublinear at infinity. Two cases will be considered: (i) f is superlinear at the origin; (ii) f does not satisfy any asymptotical property at the origin. In both situations, the existence of certain multiple weak solutions of (Pλ) are established for some λ > 0.
- Multiple solutions
- Nonlinear Schrödinger equations
- Sublinearity at infinity
ASJC Scopus subject areas
- Applied Mathematics