Nodal Solutions for a Class of Fourth-Order Two-Point Boundary Value Problems
We consider the fourth-order two-point boundary value problem u′′′′+Mu=λh(t)f(u), 0<t<1, u(0)=u(1)=u′(0)=u′(1)=0, where λ∈ℝ is a parameter, M∈(-&...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2010-01-01
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| Series: | Boundary Value Problems |
| Online Access: | http://dx.doi.org/10.1155/2010/570932 |
| Summary: | We consider the fourth-order two-point boundary value problem u′′′′+Mu=λh(t)f(u), 0<t<1, u(0)=u(1)=u′(0)=u′(1)=0, where λ∈ℝ is a parameter, M∈(-π4,π4/64) is given constant, h∈C([0,1],[0,∞)) with h(t)≢0 on any subinterval of [0,1], f∈C(ℝ,ℝ) satisfies f(u)u>0 for all u≠0, and lim⁡u→-∞f(u)/u=0, lim⁡u→+∞f(u)/u=f+∞, lim⁡u→0f(u)/u=f0 for some f+∞,f0∈(0,+∞). By using disconjugate operator theory and bifurcation techniques, we establish existence and multiplicity results of nodal solutions for the above problem. |
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| ISSN: | 1687-2762 1687-2770 |