On a class of Schrödinger-type equations with indefinite weight functions. (English summary) Comm. Partial Differential Equations 33 (2008), no. 7-9, 1368–1394. This paper is devoted to the study of entire positive solutions to the nonlinear Schrödinger equation −∆pu − λh(x)|u | p−2 u = Q(x)|u | q−2 u in RN, where λ is a real number, p < q < Np/(N − p) and 1 < p < N. The functions h and Q denote sign-changing potentials such that h ∈ LN/p (RN) ∩ L ∞ (RN) and Q ∈ L ∞ (RN). Let λ1(h) denote the lowest positive eigenvalue of −∆p and let ϕ1> 0 be the associated eigenvalue. The main results established in the present paper are the following: (i) the above problem has a positive solution provided that 0 < λ < λ1(h); (ii) if Q(x)ϕ
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