## Global Bifurcation Results for Semilinear Elliptic Equations on R N: The Fredholm Case

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Global Bifurcation Results for Semilinear Elliptic Equations on R N: The Fredholm Case
(EN)

Stavrakakis, NM
(EN)

N/A
(EN)

We prove the existence of a continuum of positive solutions for the semilinear elliptic equation -Delta u(x) = lambda g(x) f(u(x)), 0<u<1 for x epsilon R-N, lim(/x/-->+infinity)u(x)=0, which arises in population genetics, under the hypotheses that N greater than or equal to 3 and the weight g changes sign, being negative and away from zero at ca. After establishing the existence of a simple positive principal eigenvalue E., for the corresponding linearized problem, we prove the existence of a continuum of solutions lying in the space R x H-2 extended from lambda(1) to infinity. To complete this task we state a new version of the global bifurcation theory for nonlinear Fredholm (noncompact) operators and prove the compactness of the solution set of the problem. (C) 1998 Academic Press.
(EN)

journalArticle

indefinite weights
(EN)

spectral theory
(EN)

unbounded domains
(EN)

nonlinear elliptic equation
(EN)

PRINCIPAL EIGENVALUES
(EN)

Bifurcation theory
(EN)

weighted sobolev spaces
(EN)

INDEFINITE WEIGHT FUNCTION
(EN)

Fredholm (noncompact) operators
(EN)

Εθνικό Μετσόβιο Πολυτεχνείο
(EL)

National Technical University of Athens
(EN)

Journal of Differential Equations
(EN)

1998

ACADEMIC PRESS INC
(EN)

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