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1.
Under suitable conditions on , the boundary value problem

has at least one positive solution. Moreover, we also apply this main result to establish several existence theorems of multiple positive solutions for some nonlinear (elliptic) differential equations.

  相似文献

2.
The purpose of this work is to establish the timescale version of Lyapunov’s inequality as follows: Let x(t) be a nontrivial solution of
satisfying x(a)=x(b)=0. Then, under suitable conditions on p, r, a and b, we have
where p+(t)=max{p(t),0},f(t)=(ta)(bt) and satisfies
if . Here is a timescale (see below).  相似文献
3.
The nonlinear Levin's comparison theorems for nonlinear second order differential equations have been established by using a modified Levin's technique.  相似文献
4.
Sufficient conditions for the uniqueness of positive solutions of boundary value problems for quasilinear differential equations of the type
(|u′|m−2u′)′ + f(t,u,u′)=0, m 2
are established. These problems arise, for example, in the study of the m-Laplace equation in annular regions.  相似文献
5.
We consider the eigenvalue gap/ratio of the p-Laplacian eigenvalue problems, and obtain the minimizer of the eigenvalue gap for the single-well potential function. For the dual result, we also obtain the minimizer of the eigenvalue ratio for the single-barrier density function for p-Laplacian. This extends the results of the classical problem for the case p=2.  相似文献
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