Positive Solutions for a Class of Quasilinear Elliptic Equations with a Dirichlet Problem

Yanfang CHENG; Zuodong YANG

doi:10.3968/j.sms.1923845220120201.006

Positive Solutions for a Class of Quasilinear Elliptic Equations with a Dirichlet Problem

Yanfang CHENG, Zuodong YANG

Abstract

In this paper, we study the following problem -Δ_p u = h(x)u^q + f(u), u∈W_0^{1,p}(Ω), u > 0 in Ω, where Ω is a bounded smooth domain in R^N (N ≥ 3), 0 < q < 1. By using Mountain Pass Theorem, we prove that there exists at least two positive solutions under suitable assumptions on the nonlinearity. Key Words: Quasilinear elliptic equation; Positive solution; Dirichlet problem; Mountain Pass Theorem

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DOI: http://dx.doi.org/10.3968/j.sms.1923845220120201.006

DOI (PDF): http://dx.doi.org/10.3968/g1546

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