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Search: All articles in the CJM digital archive with keyword degree theory

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1. CJM Online first

Hakl, Robert; Zamora, Manuel
Periodic solutions of an indefinite singular equation arising from the Kepler problem on the sphere
We study a second-order ordinary differential equation coming from the Kepler problem on $\mathbb{S}^2$. The forcing term under consideration is a piecewise constant with singular nonlinearity which changes sign. We establish necessary and sufficient conditions to the existence and multiplicity of $T$-periodic solutions.

Keywords:singular differential equation, indefinite singularity, periodic solution, Kepler problem on $\mathbb{S}^1$, degree theory
Categories:34B16, 34C25, 70F05, 70F15

2. CJM 2006 (vol 58 pp. 449)

Agarwal, Ravi P.; Cao, Daomin; Lü, Haishen; O'Regan, Donal
Existence and Multiplicity of Positive Solutions for Singular Semipositone $p$-Laplacian Equations
Positive solutions are obtained for the boundary value problem \[\begin{cases} -( | u'| ^{p-2}u')' =\lambda f( t,u),\;t\in ( 0,1) ,p>1\\ u( 0) =u(1) =0. \end{cases} \] Here $f(t,u) \geq -M,$ ($M$ is a positive constant) for $(t,u) \in [0\mathinner{,}1] \times (0,\infty )$. We will show the existence of two positive solutions by using degree theory together with the upper-lower solution method.

Keywords:one dimensional $p$-Laplacian, positive solution, degree theory, upper and lower solution

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