Abstract
Existence of entire radial solutions to a class of quasilinear elliptic equations and systems
Highlights
The purpose of this paper is to investigate the existence of entire positive radial solutions to the following quasilinear elliptic equation div(φ1(|∇u|)∇u) + a1(|x|)φ1(|∇u|)|∇u| = b1(|x|) f (u), x ∈ RN, (1.1)
We extend the results of [25] and show existence of entire positive radial solutions to (1.1) and (1.2) for more general ai and fi
The remaining proofs are similar to that for Theorems 1.2 and 1.3
Summary
(2) when φ1(t) = ptp−2, Ψ1(t) = tp, t > 0, p > 1, ∆φ1 u = ∆pu is the p-Laplacian operator In this case, p1 = q1 = p in (S4), and k1 = l1 = p − 1 in (S5);. (3) when φ1(t) = ptp−2 + qtq−2, Ψ1(t) = tp + tq, t > 0, 1 < p < q, ∆φ1 u = ∆pu + ∆qu is called as the (p + q)-Laplacian operator, p1 = p, q1 = q in (S4), and k1 = p − 1, l1 = q − 1 in (S5);. For the existence of entire positive radial large solutions to equation (1.11). For N ≥ 3, f (u) = uγ, γ ∈ (0, 1], and b1 satisfies (S1) with b1(x) = b1(|x|), Lair and Wood [16] first showed that equation (1.11) has infinitely many entire positive radial large solutions if and only if. [1,2,3, 8, 21,22,23] and the references therein
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