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

J. F. Toland

doi:10.1090/S0002-9947-1984-0728716-3

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

J. F. Toland

Department of Mathematical Sciences

University of East Anglia

Research output: Contribution to journal › Article › peer-review

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 L_p norm of u are obtained which depend on the relative values of a and p, and the Pohozaev and Sobolev embedding constants.

Original language	English
Pages (from-to)	335-354
Number of pages	20
Journal	Transactions of the American Mathematical Society
Volume	282
Issue number	1
DOIs	https://doi.org/10.1090/S0002-9947-1984-0728716-3
Publication status	Published - Mar 1984

Keywords

A priori estimates
Global bifurcation
Singular elliptic problem

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

Access to Document

10.1090/S0002-9947-1984-0728716-3

Cite this

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AB - 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.

KW - A priori estimates

KW - Global bifurcation

KW - Singular elliptic problem

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