Multiple Positive Solutions of Semilinear Differential Equations with Singularities |
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Authors: | Lan K. Q. |
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Affiliation: | Department of Mathematics and Statistics, York University Toronto, Ontario, Canada M3J 1P3 |
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Abstract: | The existence of positive solutions of a second order differentialequation of the form z'+g(t)f(z)=0 (1.1) with the separated boundary conditions: z(0) ßz'(0)= 0 and z(1)+z'(1) = 0 has proved to be important in physicsand applied mathematics. For example, the ThomasFermiequation, where f = z3/2 and g = t1/2 (see [12, 13, 24]),so g has a singularity at 0, was developed in studies of atomicstructures (see for example, [24]) and atomic calculations [6].The separated boundary conditions are obtained from the usualThomasFermi boundary conditions by a change of variableand a normalization (see [22, 24]). The generalized EmdenFowlerequation, where f = zp, p > 0 and g is continuous (see [24,28]) arises in the fields of gas dynamics, nuclear physics,chemically reacting systems [28] and in the study of multipoletoroidal plasmas [4]. In most of these applications, the physicalinterest lies in the existence and uniqueness of positive solutions. |
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