Global bifurcation of positive solutions for a class of superlinear biharmonic equations

AbstractWe are concerned with semilinear biharmonic equations of the formwhere B denotes the unit ball in ℝN, N ≥ 1, λ > 0 is a parameter, ∂/∂ν is the outward normal derivative, f : ℝ → (0, +∞) is a continuous function that has super-linear growth at infinity. We use bifurcation theory, combined with an approximation scheme to establish the existence of an unbounded branch of positive radial solutions, which is bounded in positive λ–direction. If in addition, f satisfies certain subcritical condition, we show that the branch must bifurcate from infinity at λ = 0.Mathematics Subject Classification (2020): 35J4035G3035B3235P30Key words: Biharmonic operatorpositive radial solutionsbifurcation from infinityunbounded brancheigenvalue