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《Applied Mathematics Letters》2005,18(11):1256-1264
In this paper, we discuss the existence of positive periodic solutions to the nonlinear differential equation where is an -periodic continuous function with , is continuous and is also an -periodic function for each . Using the fixed point index theory in a cone, we get an essential existence result because of its involving the first positive eigenvalue of the linear equation with regard to the above equation. 相似文献
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《Applied Mathematics Letters》2005,18(10):1163-1169
In this work we deal with a class of second-order elliptic problems of the form , with non-homogeneous boundary condition where is the ball of radius centered at origin, are positive parameters, is an increasing function and is not identically zero on any subinterval of . We obtain via a fixed point theorem of cone expansion/compression type the existence of at least three positive radial solutions. 相似文献
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Under the assumption that , we derive necessary and sufficient conditions in terms of spectral data for (non-self-adjoint) Schrödinger operators in with periodic and antiperiodic boundary conditions to possess a Riesz basis of root vectors (i.e., eigenvectors and generalized eigenvectors spanning the range of the Riesz projection associated with the corresponding periodic and antiperiodic eigenvalues).We also discuss the case of a Schauder basis for periodic and antiperiodic Schrödinger operators in , . 相似文献
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This paper considers the IBVP of the Rosenau equation It is proved that this IBVP has a unique global distributional solution as initial data with . This is a new global well-posedness result on IBVP of the Rosenau equation with Dirichlet boundary conditions. 相似文献