A Semilinear Elliptic Problem Involving Nonlinear Boundary Condition and Sign-changing Potential
نویسنده
چکیده
In 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: −∆u+ u = λf(x)|u|q−2u in Ω, ∂u ∂ν = g(x)|u|p−2u on ∂Ω, has at least two nontrivial nonnegative solutions for λ is sufficiently small.
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