Positive solutions of nonlinear elliptic equations- existence and nonexistence of solutions with radial symmetry in lp(Rn)

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Abstract

It is shown that when r is nonincreasing, radially symmetric, continuous and bounded below by a positive constant, the solution set of the nonlinear elliptic eigenvalue problem (FORMULA PRESENTED) contains a continuum (f of nontrivial solutions which is unbounded in (FORMULA PRESENTED) for all p≥ Various estimates of the Lp norm of u are obtained which depend on the relative values of a and p, and the Pohozaev and Sobolev embedding constants.

Original languageEnglish
Pages (from-to)335-354
Number of pages20
JournalTransactions of the American Mathematical Society
Volume282
Issue number1
DOIs
Publication statusPublished - Mar 1984

Keywords

  • A priori estimates
  • Global bifurcation
  • Singular elliptic problem

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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