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Two-point higher-order BVPs with singularities in phase variables |
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| Authors: | R P Agarwal D O'Regan I Rach nkov S Stan k |
| Affiliation: | Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL 32901, U.S.A. Department of Mathematics, National University of Ireland, Galway, Ireland Department of Mathematical Analysis, Faculty of Science Palacký University, Tomkova 40, 779 00, Olomouc, Czech Republic |
| Abstract: | The existence of solutions for singular higher-order differential equations with the Lidstone or the (n,p) boundary conditions is proved. The right-hand sides of differential equations can have singularities in the zero value of their phase variables and so higher derivatives of solutions changing their signs can pass through these singularities. Proofs are based on the method of a priori estimates, the degree theory arguments and on Vitali's convergence theorem. |
| Keywords: | Author Keywords: Singular higher-order differential equation Lidstone boundary conditions (np) boundary conditions existence regularization topological degree Vitali's theorem |
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