Wu, Tsung-fang2021-07-202021-07-202006-10-17Wu, T. F. (2006). A semilinear elliptic problem involving nonlinear boundary condition and sign-changing potential. <i>Electronic Journal of Differential Equations, 2006</i>(131), pp. 1-15.1072-6691https://hdl.handle.net/10877/14004In this paper, we study the multiplicity of nontrivial nonnegative solutions for a semilinear elliptic equation involving nonlinear boundary condition and sign-changing potential. With the help of the Nehari manifold, we prove that the semilinear elliptic equation: -Δu + u = λƒ(x)|u|q-2u in Ω, ∂u/∂v = g(x)|u|p-2u on ∂Ω, has at least two nontrivial nonnegative solutions for λ is sufficiently small.Text15 pages1 file (.pdf)enAttribution 4.0 InternationalSemilinear elliptic equationsNehari manifoldNonlinear boundary conditionArticle