In this paper we consider the quasilinear elliptic equation (1) div(|∇u|m-2∇u) + f(u) = 0 where n > m > 1. We obtain a necessary and sufficient condition for the existence of positive radial solutions u = u(r) on [r0, ∞), where r0 > 0. If f satisfies a further condition, then Eq. (1) possesses infinitely many singular ground state solutions u(r) satisfying u(r) ∼ r-(n-m)/m-1 at ∞ and u(r) → ∞ as r → 0+. We also obtain some important conclusions via our main results.
- Ground state
- Quasilinear elliptic equations
- Singular solutions
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