Solvability of a Fourth-Order Boundary Value Problem with Integral Boundary Conditions
We investigate the existence of solutions and positive solutions for a nonlinear fourth-order differential equation with integral boundary conditions of the form x(4)(t)=f(t,x(t),x′(t),x′′(t),x′′′(t)), t∈[0,1], x(0)=x′(1)=0, x′′(0)=∫01h(s,x(s),x′(s),x′′(s))ds, x′′′(1)=0, where f∈C([0,1]×ℝ4), h∈C([0,...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/782363 |
| Summary: | We investigate the existence of solutions and positive solutions
for a nonlinear fourth-order differential equation with integral boundary conditions of the
form x(4)(t)=f(t,x(t),x′(t),x′′(t),x′′′(t)), t∈[0,1], x(0)=x′(1)=0, x′′(0)=∫01h(s,x(s),x′(s),x′′(s))ds, x′′′(1)=0, where f∈C([0,1]×ℝ4), h∈C([0,1]×ℝ3). By using a fixed point theorem due to D.
O'Regan, the existence of solutions and positive solutions for the previous boundary value
problems is obtained. Meanwhile, as applications, some examples are given to illustrate
our results. |
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| ISSN: | 1110-757X 1687-0042 |