Compact components of positive solutions for superlinear indefinite elliptic problems of mixed type (Q1882611)

The main purpose of this paper is to give sufficient conditions on the potentials \(W(x),a(x)\in L^\infty(\Omega)\) and the nonlinearity \(F(x,u)\) so that the superlinear indefinite weighted elliptic mixed boundary value problem \[ Lu= \lambda W(x)u-a(x)F(x,u)u\text{ in }\Omega\quad B(b)u =0\text{ on }\partial\Omega \tag{1} \] has a component of positive solutions of (1) bifurcating from the trivial branch \((\lambda,u)= (\lambda,0)\) at two bifurcation values of \(\lambda\), \(\sigma_1^{(1)}, \sigma_1^{(2)},\sigma_1^{(1)}\neq\sigma_1^{(2)}\) which are simple eigenvalues of a certain linear weighted elliptic mixed boundary value problem.