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Pairs of positive periodic solutions of nonlinear ODEs with indefinite weight: a topological degree approach for the super–sublinear case
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- Journal:
- Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 146 / Issue 3 / June 2016
- Published online by Cambridge University Press:
- 16 May 2016, pp. 449-474
- Print publication:
- June 2016
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We study the periodic and Neumann boundary-value problems associated with the second-order nonlinear differential equation
where
is a sublinear function at infinity having superlinear growth at zero. We prove the existence of two positive solutions when
and λ > 0 is sufficiently large. Our approach is based on Mawhin's coincidence degree theory and index computations.
is a sublinear function at infinity having superlinear growth at zero. We prove the existence of two positive solutions when
MULTIPLE POSITIVE SOLUTIONS OF RESONANT AND NON-RESONANT NON-LOCAL FOURTH-ORDER BOUNDARY VALUE PROBLEMS
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- Journal:
- Glasgow Mathematical Journal / Volume 54 / Issue 1 / January 2012
- Published online by Cambridge University Press:
- 09 December 2011, pp. 225-240
- Print publication:
- January 2012
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We study the existence of positive solutions for equations of the form
where 0 < ω < π, subject to various non-local boundary conditions defined in terms of the Riemann–Stieltjes integrals. We prove the existence and multiplicity of positive solutions for these boundary value problems in both resonant and non-resonant cases. We discuss the resonant case by making a shift and considering an equivalent non-resonant problem.
