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We study the existence of positive solutions of second order nonlinear separated boundary value problems of superlinear as well as sublinear type without imposing monotonicity restrictions on the problem. The type of problem investigated cannot be analyzed using the linearization about the trivial solution because either it does not exist (the sublinear case) or is trivial (the superlinear case). The results follow from a known fixed point theorem by noticing that the concavity of the solutions provides an important condition for the applicability of the fixed point result.
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참고문헌 (7)
참고문헌 신청
C. D. Luning / 1977 / An iterative technique for solution of the Thomas-Fermi equation utilizing a nonlinear eigenvalue problem / Quart. Appl. Math 35 (2) : 257 ~ 268
C. D. Luning / 1981 / Convergence of Berriman's Iterative Method for Some Emden-Fowler Equations / J. Math. Phys 22 (8) : 1591 ~ 1595
G. B. Gustafson / 1975 / Methods of Nonlinear Analysis in the Theory of Differential Equations / Department of Mathematics, University of Utah
J. A. Gatica / 1977 / Fixed point techniques in a cone with applications / J. Math. Anal. Appl 61 (1) : 58 ~ 71
J. A. Gatica / 1990 / Iterative procedures for nonlinear second order boundary value problems / Ann. Mat. Pura Appl 157 : 1 ~ 25
C. D. Luning / 1981 / Convergence of Berriman's Iterative Method for Some Emden-Fowler Equations / J. Math. Phys 22 (8) : 1591 ~ 1595
G. B. Gustafson / 1975 / Methods of Nonlinear Analysis in the Theory of Differential Equations / Department of Mathematics, University of Utah
J. A. Gatica / 1977 / Fixed point techniques in a cone with applications / J. Math. Anal. Appl 61 (1) : 58 ~ 71
J. A. Gatica / 1990 / Iterative procedures for nonlinear second order boundary value problems / Ann. Mat. Pura Appl 157 : 1 ~ 25
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