Non-local second-order boundary value problems with derivative-dependent nonlinearity
J. R. L. Webb
2021Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences10 citationsDOI
Abstract
We prove the existence of multiple positive solutions of nonlinear second-order nonlocal boundary value problems with nonlinear term having derivative dependence. We allow the nonlinearity to grow quadratically with respect to derivatives. We obtain a priori bounds for norms of derivatives by using a recently obtained Gronwall-type inequality. Three examples illustrate some of the results. This article is part of the theme issue ‘Topological degree and fixed point theories in differential and difference equations’.
Topics & Concepts
MathematicsNonlinear systemA priori and a posterioriA priori estimateQuadratic growthBoundary value problemType (biology)Applied mathematicsDerivative (finance)Order (exchange)Mathematical analysisTerm (time)Second derivativeValue (mathematics)PhysicsQuantum mechanicsEcologyBiologyStatisticsPhilosophyEconomicsFinancial economicsFinanceEpistemologyNonlinear Differential Equations AnalysisFractional Differential Equations SolutionsDifferential Equations and Boundary Problems