Differential and Integral Equations

Positive solutions for a two-point nonlinear boundary value problem with applications to semilinear elliptic equations

Lew Lefton and Jairo Santanilla

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Abstract

Sharp existence results are given for positive solutions to the boundary value problem $v''+g(t,v) =0$, $v(0)= v(t_0)=0$, where $g(t,v)$ is allowed to be singular at both $t=0$ and $t=t_0$. These results are applied to radial solutions of the semilinear elliptic problem $\Delta u +f(r,u)= 0$ on a ball. Examples and corollaries illustrate the wide class of equations to which the results apply. The proofs use the Mountain Pass Lemma in conjunction with some delicate estimates, which allow the treatment of singular equations.

Article information

Source
Differential Integral Equations, Volume 9, Number 6 (1996), 1293-1304.

Dates
First available in Project Euclid: 6 May 2013

Permanent link to this document
https://projecteuclid.org/euclid.die/1367846902

Mathematical Reviews number (MathSciNet)
MR1409929

Zentralblatt MATH identifier
0879.34027

Subjects
Primary: 35J65: Nonlinear boundary value problems for linear elliptic equations
Secondary: 35B05: Oscillation, zeros of solutions, mean value theorems, etc.

Citation

Lefton, Lew; Santanilla, Jairo. Positive solutions for a two-point nonlinear boundary value problem with applications to semilinear elliptic equations. Differential Integral Equations 9 (1996), no. 6, 1293--1304. https://projecteuclid.org/euclid.die/1367846902


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