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| This paper is concerned with the existence of multiple positive solutions for(ω(t)ψp(u'(t)))'+h(t)f(t,u(t),u'(t))=o,t∈(0,+∞);u(0)/1+l(0)=βlim t→0+(ψ -1 p(ω)u')(t),lim t→+∞(ψ -1 p(ω)u')(t)=0; where ω∈C((0,+∞),(0,+∞)), ψp(s)=|s|p-2, p>1,β≥0, both h(t) and f(t,u,v) are nonnegative continuous functions thatmay be singular at t=0, l(t)=∣t0 ψ p -1(1/ω)ds. By usinga fixed point theorem due to Avery and Peterson, some sufficient conditions forthe existence of at least three positive solutions to the above problem areestablished. The interesting points are that the weight function $omega$ isassumed to satisfy ψ p -1(1/ω)∈L1(0,b) for all b∈(0,+∞)$rather than ψ p -1(1/ω)∈L1(0,+∞) and the nonlinear term f is involved with the first-order derivative explicitly. |
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| Keywords:Weighted p-Laplacian; Three Positive Solutions; Fixed Point Theorem; Weighted Banach Space |
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