On the existence and multiplicity of positive solutions of the pp-Laplacian separated boundary value problem
(1997) Differential and Integral Equations — Vol. 10, p. 1093-1112 (1997)
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- Abstract
- Using the lower and upper solutions method together with degree theory, we study the existence and multiplicity of positive solutions for the problem (φp(u′))′+f(t,u)=0, a1φp(u(a))−a2φp(u′(a))=0, b1φp(u(b))+b2φp(u′(b))=0, (φp(u′))′+f(t,u)=0, a1φp(u(a))−a2φp(u′(a))=0, b1φp(u(b))+b2φp(u′(b))=0, where φp(s):=|s|p−2s,p>1φp(s):=|s|p−2s,p>1, a1,b1∈Ra1,b1∈R, a2,b2∈R+a2,b2∈R+, a21+a22>0a12+a22>0, b21+b22>0.b12+b22>0. The function ff satisfies assumptions related to the classically called sublinear, superlinear, subsuperlinear, or supersublinear cases. Our results improve the recent ones of L.H. Erbe-H. Wang ([21]) and L.H. Erbe-S. Hu-H. Wang ([20]).
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Ben-Naoum, A. K., & de coster, C. (1997). On the existence and multiplicity of positive solutions of the pp-Laplacian separated boundary value problem. Differential and Integral Equations, 10, 1093-1112. https://hdl.handle.net/2078.5/252026 (Original work published 1997)