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Existence, multiplicity and uniqueness results for a second order m-point boundary value problem

Existence, multiplicity and uniqueness results for a secondorder m-point boundary value problem

Sanyang Liu|Yuqiang Feng
대한수학회 (The Korean Mathematical Society)|2004.08|대한수학회보 (Bulletin of the KMS)|제41권 제3호|pp. 483-492

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Abstract

Let f:[0,1]times [0,infty)rightarrow [0,infty) be continuousand ain C([0,1],[0,infty)),and let xi_{i}in (0,1) with0<xi_{1} <xi_{2}<cdots<xi_{m-2}<1,a_{i}, b_{i}in [0,infty)with 0<sum_{i=1}^{m-2}a_{i}<1 andsum_{i=1}^{m-2}b_{i}<1.This paper is concerned with thefollowing m-point boundary value problem: x^{''}(t)+a(t)f(t,x(t))=0, tin (0,1),x^{'}(0)=sum_{i=1}^{m-2}b_{i}x^{'}(xi_{i}),x(1)=sum_{i=1}^{m-2}a_{i}x(xi_{i}) . The existence,multiplicity and uniqueness of positive solutions of this problemarediscussed with the help of two fixed point theorems in cones, respectively.

참고문헌 (10)

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  2. "Existence theorems for a second order m-point boundary valueproblem", 211, pp.545~555 (1997)
  3. "Solvability of a m-point boundary value problems withnonlinear growth", 212, pp.467~480 (1997)
  4. "Existence of solutions of nonlinear m-pointboundary-value problems", 256, pp.556~567 (2001)
  5. "Existence and multiplicity of positive radial solutions for aclass of nonlinear elliptic equations in annular domains", pp.633~638 (2001)
  6. "The fixedpoint theorem and application for some decreasing operator", 42, pp.193~196 (1999)
  7. "Nonlinear Problems in Abstract Cones" (1998), Academic Press
  8. "Fixed point equations and nonlinear eigenvalue problems in ordered Banachspaces", 18, pp.620~ (1976)
  9. "New fixed point theorems of mixed monotone operators andapplications", 204, pp.307~319 (1996)
  10. "New fixed point theorems of mixed monotone operators andapplications", 204, pp.307~319 (1996)

관련 논문AI추천

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