Positive Solutions of a Nonlinear Fourth-Order Dynamic Eigenvalue Problem on Time Scales
Let T be a time scale and a,b∈T, a<ρ2(b). We study the nonlinear fourth-order eigenvalue problem on T, uΔ4(t)=λh(t)f(u(t),uΔ2(t)), t∈[a,ρ2(b)]T, u(a)=uΔ(σ(b))=uΔ2(a)=uΔ3(ρ(b))=0 and obtain the existence and nonexistence of positive solutions when 0<λ≤λ* and λ>λ*, respectively, for some λ*....
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/798796 |
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| Summary: | Let T be a time scale and a,b∈T, a<ρ2(b). We study the nonlinear fourth-order eigenvalue problem on T, uΔ4(t)=λh(t)f(u(t),uΔ2(t)), t∈[a,ρ2(b)]T, u(a)=uΔ(σ(b))=uΔ2(a)=uΔ3(ρ(b))=0 and obtain the existence and nonexistence of positive solutions when 0<λ≤λ* and λ>λ*, respectively, for some λ*. The main tools to prove the existence results are the Schauder fixed point theorem and the upper and lower solution method. |
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| ISSN: | 1085-3375 1687-0409 |