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Topological Methods in Nonlinear Analysis

Compare this space with the one without the dirichlet flag:. Thus, the dirichlet flag did not change ndof. The space fs2 without dirichlet flag has only free dofs no dirichlet dofs. The other space fes has a few dofs that are marked as not free.

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These are the dofs that are located on the boundary regions we marked as dirichlet. We use the standard technique of reducing a problem with essential non-homogeneous boundary conditions to one with homogeneous boundary condition using an extension. Split the solution. These are the issues to consider in this approach:.

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The keyword BND tells Set that g need only be interpolated on those parts of the boundary that are marked dirichlet. I searched for literature and get Narrow escape problem but there they assume that the absorbing boundary is quite small as compared to the reflective one. What if the absorbing boundary is not that small, is there a reference that deals specifically with mixed boundary value problems.

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On Dirichlet's Boundary Value Problem: LP-Theory Based on a Generalization of Garding's Inequality

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Ross, An introduction to the fractional calculus and fractional differential equations, John Wiley and Sons, Inc. Samko, A. Kilbas and O. Li and Q. Dai, Nonlinear fractional differential equations with nonlocal integral boundary conditions, Bound.

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Lakshmikantham and A. Vatsala, General uniqueness and monotone iterative technique for fractional differential equations.

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Han, H. Gao, Existence of positive solutions for eigenvalue problem of nonlinear fractional differential equations. Sun, M. Zhao, Positive solutions for a class of fractional differential equations with integral boundary conditions. Lett, 34 , Xu, Fractional boundary value problems with integral and anti-periodic boundary conditions. Qiao and Z. Doi: x, , 9 pages. Bai, W. Sun and W.

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Zhang, Positive solutions for boundary value problems of singular fractional differential equations. Positive solutions for nonlinear fractional differential equation with nonlocal boundary conditions. Universal Journal of Mathematics and Applications , 1 1 ,