Positive solutions for a nonhomogeneous Kirchhoff equation with the asymptotical nonlinearity in \(R^3\)
Summary: We study the following nonhomogeneous Kirchhoff equation: \(-(a + b \int_{R^3} | \nabla u |^2 d x) \Delta u + u = k(x) f(u) + h(x)\), \(x \in R^3\), \(u \in H^1(R^3)\), \(u > 0\), \(x \in R^3\), where \(f\) is asymptotically linear with respect to \(t\) at infinity. Under appropriate assumptions on \(k, f\), and \(h\), existence of two positive solutions is proved by using the Ekeland's variational principle and the Mountain Pass Theorem in critical point theory.
scientific article; zbMATH DE number 7022928
scientific article