Abstract
We study the global bifurcation diagram of the following semilinear elliptic problem mainly in the case n ≥ 3. A is the usual Laplace operator.
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References
C. Bandle, M.A. Pozio and A. Tesei, Existence and uniqueness of solutions of nonlinear Neumann problems, Math. Zeitschrift 199(1988), 257–278.
K.J. Brown, C. Cosner and J. Fleckinger, Principal eigenvalues for problems with indefinite weight function on ℝn, preprint (1989).
K.J. Brown and P. Hess, Stability and uniqueness of positive solutions for a semilinear elliptic boundary value problem, preprint (1989).
K.J. Brown, S.S. Lin and A. Tertikas, Existence and nonexistence of steady-state solutions for a selection-migration model in population genetics, J. Math. Biol. 27(1989), 91–104.
K.J. Brown and A. Tertikas, On the bifurcation of radially symmetric steady-states solutions arising in population genetics, to appear in SIAM J. Math. Anal.
P.C. Fife and L.A. Peletier, Nonlinear diffusion in population genetics, Arch. Rat. Mech. Anal. 64(1977), 93–109.
W.H. Fleming, A selection-migration model in population genetics, J. Math. Biol. 2(1975), 219–233.
B. Gidas, W.N. Ni and L. Nirenberg, Summeiry of positive solutions of nonlinear elliptic equations in ℝn, Math. Anal. Appl., part A, Adv. Math. Suppl. Studies 7A(1981), 369–402.
P. Hess and T. Kato, On some linear and nonlinear eigenvalue problems with an indefinite weight function, Comm. Partial Differential Equations 5(1980), 999–1030.
H. Matano, L∞ stability of an exponentially decreasing solution of the problem Δu + f(x,u) = 0 in ℝn, Japan J. Appl. Math. 2(1985), 85–110.
N. Meyers and J. Serrin, The exterior Dirichlet problem for secondorder elliptic partial differential equations, J. Math. Mech. 9(1960), 513–538.
W.M. Ni, On the elliptic equation Δu + k(x)u (n+2)/(n-2) its generalizations and applications in geometry, Indiana Univ. J.31(1982), 493–
L.A. Peletier and J. Serrin, Uniqueness of positive solutions of semilinear equations in ℝn, Arch. Rat. Mech. Anal. 81(1983), 181–197.
L.A. Peletier and A. Tesei, Global bifurcation and attractivity of stationary solutions of a degenerate diffusion equation, Adv. Appl. Math. 7(1986), 435–454.
M. Slatkin, Gene flow and selection in a cline, Genetics 75(1973), 733–756.
N. Stavrakakis, J. Stratis and A. Tertikas, in preparation.
CA. Stuart, Bifurcation in L p(ℝn) for a semilinear elliptic equation, Proc. London Math. Soc. 57(1988), 511–541.
A. Tertikas, Semilinear elliptic equations on ℝn, Ph.D. Thesis, Heriot-Watt University, 1987.
A. Tertikas, Existence and Uniqueness of solutions for a nonlinear diffusion problem arising in population genetics, Arch. Rat. Mech. Anal. 4(1988), 289–317.
A. Tertikas, Uniqueness of solutions for problems arising in population genetics, in Differential Equations, C.M. Dafermos, G. Ladas and G. Papanicolaou, Eds. Lecture Notes in Pure and Applied Mathematics, 118(1989), 667–672.
A. Tertikas, J.F. Toland, Graph intersection and uniqueness results for some nonlinear elliptic problems, to appear in J. Diff. Eqs.
J.F. Toland, Positive solutions of nonlinear elliptic equations-existence and nonexistence of solutions with radial symmetry in L p(ℝn), Trans. Amer. Math. Soc. 282(1984), 335–354.
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Tertikas, A. (1992). Global Bifurcation of Positive Solutions in ℝn . In: Lloyd, N.G., Ni, W.M., Peletier, L.A., Serrin, J. (eds) Nonlinear Diffusion Equations and Their Equilibrium States, 3. Progress in Nonlinear Differential Equations and Their Applications, vol 7. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0393-3_35
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DOI: https://doi.org/10.1007/978-1-4612-0393-3_35
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