Extremal solutions to fourth order discontinuous functional boundary value problems |
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| Authors: | Alberto Cabada João Fialho Feliz Minhós |
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| Institution: | 1. +34 881 81 3206+34 881 81 3197;2. Departamento de Análise Matemática, Facultade de Matemáticas, Universidade de Santiago de Compostela, , Spain;3. +1 242 302 4300+1 242 302 4300;4. Research Center in Mathematics and Applications (CIMA‐UE), University of évora, , 7000 évora, Portugal;5. Department of Mathematics, School of Sciences and Technology, University of évora, , 7000 évora, Portugal |
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| Abstract: | In this paper, given  a L1‐Carathéodory function, it is considered the functional fourth order equation ![urn:x-wiley:dummy:mana201100239:equation:mana201100239-math-0002]( "urn:x-wiley:dummy:mana201100239:equation:mana201100239-math-0002") together with the nonlinear functional boundary conditions ![urn:x-wiley:dummy:mana201100239:equation:mana201100239-math-0003]( "urn:x-wiley:dummy:mana201100239:equation:mana201100239-math-0003") Here  ,  , satisfy some adequate monotonicity assumptions and are not necessarily continuous functions. It will be proved an existence and location result in presence of non ordered lower and upper solutions. |
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| Keywords: | Functional problems extremal solutions Green's functions lower and upper solutions 34B15 34B10 34K10 |
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