Multiple Solutions for Semilinear Elliptic Equations with Sign-changing Potential and Nonlinearity

In this article, we study the multiplicity of solutions for the semilinear elliptic equation −∆u + a(x)u = f(x, u), x ∈ Ω, u = 0, x ∈ ∂Ω, where Ω ⊂ RN (N ≥ 3), the potential a(x) satisfies suitable integrability conditions, and the primitive of the nonlinearity f is of super-quadratic growth near infinity and is allowed to change sign. Our super-quadratic… CONTINUE READING