Multiple positive solutions for semilinear elliptic equations in \(\mathbb R^N\) involving concave-convex nonlinearities and sign-changing weight functions
Summary: We study the existence and multiplicity of positive solutions to the semilinear elliptic equation \[ -\Delta u+u=\lambda a(x)|u|^{q-2}u+b(x)|u|^{p-2}u \;\text{ in } {\mathbb R}^N, \;\;u\in H^1({\mathbb R}^N), \] where \(\lambda>0\), \(1<q<2<p<2^*\) \((2^*=2N/(N-2))\) if \(N\geq3\), \(2^*=\infty\) if \(N=1,2\), \(a(x)\), \(b(x)\) satisfy suitable conditions, and \(a(x)\) may change sign in \({\mathbb R}^N\).
scientific article; zbMATH DE number 5791633
scientific article