Phase plane analysis for radial solutions to supercritical quasilinear elliptic equations in a ball

We consider the following problem equation(0.1){Δpu+λu+f(u,r)=0u>0in  B,andu=0on  ∂B where BB is the unitary ball in RnRn. Merle and Peletier considered the classical Laplace case p=2p=2, and proved the existence of a unique value λ0∗ for which a radial singular positive solution exists, assuming f(u,r)=uq−1f(u,r)=uq−1 and q>2∗≔2nn−2. Then Dolbeault and Flores proved that, if q>2∗q>2∗ but qq is smaller than the Joseph–Lundgren exponent σ∗σ∗, then there is an unbounded sequence of radial positive classical solutions for (0.1), which accumulate at λ=λ0∗, again for p=2p=2.We extend both Merle–Peletier and Dolbeault–Flores results to the pp-Laplace setting with the technical restriction 1