Positive Solutions for Integral Boundary Value Problem with <it>ϕ</it>-Laplacian Operator
<p/> <p>We consider the existence, multiplicity of positive solutions for the integral boundary value problem with <inline-formula> <graphic file="1687-2770-2011-827510-i1.gif"/></inline-formula>-Laplacian <inline-formula> <graphic file="1687-277...
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2011-01-01
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| Series: | Boundary Value Problems |
| Online Access: | http://www.boundaryvalueproblems.com/content/2011/827510 |
| Summary: | <p/> <p>We consider the existence, multiplicity of positive solutions for the integral boundary value problem with <inline-formula> <graphic file="1687-2770-2011-827510-i1.gif"/></inline-formula>-Laplacian <inline-formula> <graphic file="1687-2770-2011-827510-i2.gif"/></inline-formula>, <inline-formula> <graphic file="1687-2770-2011-827510-i3.gif"/></inline-formula>, <inline-formula> <graphic file="1687-2770-2011-827510-i4.gif"/></inline-formula>, <inline-formula> <graphic file="1687-2770-2011-827510-i5.gif"/></inline-formula>, where <inline-formula> <graphic file="1687-2770-2011-827510-i6.gif"/></inline-formula> is an odd, increasing homeomorphism from <inline-formula> <graphic file="1687-2770-2011-827510-i7.gif"/></inline-formula> onto <inline-formula> <graphic file="1687-2770-2011-827510-i8.gif"/></inline-formula>. We show that it has at least one, two, or three positive solutions under some assumptions by applying fixed point theorems. The interesting point is that the nonlinear term <inline-formula> <graphic file="1687-2770-2011-827510-i9.gif"/></inline-formula> is involved with the first-order derivative explicitly.</p> |
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| ISSN: | 1687-2762 1687-2770 |