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### Open Access Journals

PROC

The authors investigate the asymptotic behavior of solutions of the damped nonlinear oscillator equation
$$x''+ a(t)|x'|^\alpha \sgn(x') + f(x)=0, $$
where $uf(u) > 0$ for $u \neq 0$, $a(t)\geq 0$, and $\alpha\geq 1$. The case $\alpha=1$ has been investigated by a number of other authors. There are also some results for the case $\alpha>1$, but they are not really based on the
power $\alpha$, although it plays an essential role in the behavior of the solutions.
In this paper, we give new attractivity results for the large damping case, $a(t) \geq a_0 > 0$, that improve previously known results. Our conditions involve the power $\alpha$ in such a way that our results reduce directly to known conditions in the case $\alpha=1$. Some open problems for future research are also indicated.

PROC

The authors consider the boundary value problem
$$ \begin{cases} u'''(t) = q(t)f(u), \quad 0 < t < 1, \\
u(0) = u'(p) = u''(1) = 0,
\end{cases} $$
where $p \in(\frac{1}{2},1)$ is a constant. They give sufficient conditions for the existence of multiple positive solutions to this problem. In so doing, they are able to improve some recent results on this problem. Examples are included to illustrate the results.

PROC

Please refer to Full Text.

PROC

We consider the boundary value problem with nonhomogeneous
three-point boundary condition
Sufficient conditions are obtained for the existence and uniqueness of a positive
solution. The dependence of the solution on the parameter $\lambda$ is also studied.
This work extends and improves some recent results in the literature on the
above problem, especially those in the paper [L. Kong, D. Piao, and L. Wang,
Positive solutions for third order boundary value problems with $p$-Laplacian,
Result. Math. 55 (2009) 111{128].

PROC

The authors study a type of nonlinear fractional boundary value problem with nonlocal boundary conditions. An associated Green's function is constructed. Then a criterion for the existence of at least one positive solution is obtained by using fixed point theory on cones.

DCDS-S

We consider a nonlocal boundary value problem for a third order differential equation. Sufficient conditions for the existence and nonexistence of positive solutions for the problem are obtained. The results are illustrated with some examples.

PROC

In this paper, by using the dual least action principle, the authors investigate the existence of solutions to a multi-point boundary value problem for a second-order differential system with $p$-Laplacian.

PROC

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PROC

The authors study a higher order three point boundary value problem. Estimates for positive solutions are given; these estimates improve some recent results in the literature. Using these estimates, new sufficient conditions for the existence and nonexistence of positive solutions of the problem are obtained. An example illustrating the results is included.

PROC

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