American Institute of Mathematical Sciences

Journals

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].
keywords: boundary value problems Positive solutions uniqueness dependence on a parameter
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.
keywords: fractional calculus. positive solution Green's function
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.
keywords: existence of positive solutions nonexistence of positive solutions nonlinear equations Boundary value problems nonlocal problems.
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.
keywords: dual least action principle. Multi-point boundary value problem critical point theory
PROC
keywords: impulses. Oscillation second order nonlinear systems
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.
keywords: attractivity nonlinear damping monotonicity. Second order equations
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.
keywords: third order equations. three point problems nonlinear equations existence of positive solutions Boundary value problems nonexistence of positive solutions
PROC
keywords: nonlinear limit-point square integrable solutions. nonoscillatory solutions nonlinear limit-circle oscillatory solutions
PROC