A limit equation and bifurcation diagrams of semilinear elliptic equations with general supercritical growth |
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Authors: | Yasuhito Miyamoto |
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Institution: | Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, Japan |
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Abstract: | We study radial solutions of the semilinear elliptic equation under rather general growth conditions on f. We construct a radial singular solution and study the intersection number between the singular solution and a regular solution. An application to bifurcation problems of elliptic Dirichlet problems is given. To this end, we derive a certain limit equation from the original equation at infinity, using a generalized similarity transformation. Through a generalized Cole–Hopf transformation, all the limit equations can be reduced into two typical cases, i.e., and . |
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Keywords: | primary 35J25 35B32 secondary 35J61 34C10 Singular solution Morse index Infinitely many positive solutions Joseph–Lundgren exponent |
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