in this paper, we investigate the existence of positive solutions for the ellipticequation $delta^{2},u+c(x)u = lambda f(u)$ on a bounded smooth domain $omega$ of $r^{n}$, $ngeq2$, with navier boundary conditions. we show that there exists an extremal parameter$lambda^{ast}>0$ such that for $lambda< lambda^{ast}$, the above problem has a regular solution butfor $lambda> lambda^{ast}$, the probl...

in this paper, we prove the existence and uniqueness results to the random fractional functional differential equations under assumptions more general than the lipschitz type condition. moreover, the distance between exact solution and appropriate solution, and the existence extremal solution of the problem is also considered.

In this paper, we prove the existence and uniqueness results to the random fractional functional differential equations under assumptions more general than the Lipschitz type condition. Moreover, the distance between exact solution and appropriate solution, and the existence extremal solution of the problem is also considered.

in this paper, we study the existence of extremal solutions forimpulsive delay fuzzy integrodifferential equations in$n$-dimensional fuzzy vector space, by using monotone method. weshow that obtained result is an extension of the result ofrodr'{i}guez-l'{o}pez cite{rod2} to impulsive delay fuzzyintegrodifferential equations in $n$-dimensional fuzzy vector space.

in this paper, some basic results concerning strict, nonstrict inequalities, local existence theorem and differential inequalities  have been proved for an ivp of first order hybrid  random differential equations with the linear perturbation of second type. a comparison theorem is proved and  applied to prove the uniqueness of random solution for the considered perturbed random differential equ...

If string theory describes nature, then charged black holes are not described by the Reissner-Nordstrøm solution. This solution must be modified to include a massive dilaton. In the limit of vanishing dilaton mass, the new solution can be found by a generalization of the Harrison transformation for the Einstein-Maxwell equations. These two solution generating transformations and the resulting b...

in this article, we prove the existence of extremal positive solution for the distributed order fractional hybrid differential equation$$int_{0}^{1}b(q)d^{q}[frac{x(t)}{f(t,x(t))}]dq=g(t,x(t)),$$using a fixed point theorem in the banach algebras. this proof is given in two cases of the continuous and discontinuous function $g$, under the generalized lipschitz and caratheodory conditions.

 In this paper, some basic results concerning strict, nonstrict inequalities, local existence theorem and differential inequalities  have been proved for an IVP of first order hybrid  random differential equations with the linear perturbation of second type. A comparison theorem is proved and  applied to prove the uniqueness of random solution for the considered perturbed random differential eq...

We study the extremal solution for the problem (−∆)u = λf(u) in Ω, u ≡ 0 in R \ Ω, where λ > 0 is a parameter and s ∈ (0, 1). We extend some well known results for the extremal solution when the operator is the Laplacian to this nonlocal case. For general convex nonlinearities we prove that the extremal solution is bounded in dimensions n < 4s. We also show that, for exponential and power-like ...

We study the phases of near-extremal branes on a circle, by which we mean near-extremal branes of string theory and M-theory with a circle in their transverse space. We find a map that takes any static and neutral Kaluza-Klein black hole, i.e. any static and neutral black hole on Minkowski-space times a circle Md×S1, and map it to a corresponding solution for a near-extremal brane on a circle. ...