In this paper, we study the existence and uniqueness of solutions and controllability for the semilinear fuzzy integrodifferential equations in n-dimensional fuzzy vector space (EN ) n by using Banach fixed point theorem. That is an extension of the result of Park et al. [J.H. Park, J.S. Park and Y.C. Kwun, Controllability for the semilinear fuzzy integrodifferential equations with nonlocal con...

We consider a semilinear elliptic equation ∆u+ λf(u) = 0, x ∈ Ω, ∂u

Some oscillation criteria for the second order semilinear elliptic differential equation

We study the internal controllability of the semilinear wave equation vtt(x, t)−∆v(x, t) + f(x, v(x, t)) = 1ωu(x, t) for some nonlinearities f which can produce several non-trivial steady states. One of the usual hypotheses to get global controllability, is to assume that f(x, v)v ≥ 0. In this case, a stabilisation term u = γ(x)vt makes any solution converging to zero. The global controllabilit...

This paper is contributed to the Cauchy problem  ∂u ∂t = ∆u+K(|x|)u p in R × (0, T ), u(x, 0) = φ(x) in R, (0.1) with initial function φ 6≡ 0. The stability and instability of the positive radical steady states, which are positive solutions of ∆u+K(|x|)u = 0, (0.2) has been discussed with different assumption on K(x) and φ under the norm ∗Research supported in part by the Natural Science...

In this paper, we study the existence and nonexistence of multiple positive solutions for problem   ∆u+K(x)up = 0 in Ω. u > 0 in Ω, u ∈ H1 loc(Ω) ∩ C(Ω). u ∣∣ ∂Ω = 0, u → μ > 0 as |x| → ∞ where Ω = RN \ ω is an exterior domain in RN , ω ⊂ RN is a bounded domain with smooth boundary and N > 2. μ ≥ 0, p > 1 are some given constants. K(x) satisfies: K(x) ∈ Cα loc(Ω) and ∃C, ,M > 0 such t...

In this article, we analyze the boundary behavior of solutions to the boundary blow-up elliptic problem ∆u = b(x)f(u), u ≥ 0, x ∈ Ω, u|∂Ω =∞, where Ω is a bounded domain with smooth boundary in RN , f(u) grows slower than any up (p > 1) at infinity, and b ∈ Cα(Ω̄) which is non-negative in Ω and positive near ∂Ω, may be vanishing on the boundary.

We consider the following superlinear elliptic equation on S ε∆Snu− u + u = 0 in S, u > 0 in S where ∆Sn is the Laplace-Beltrami operator on S. We prove that for any k = 1, ..., n−1, there exists pk > 1 such that for 1 < p < pk and ε sufficiently small, there exist at least n − k positive solutions concentrating on k−dimensional subset of the equator. We also discuss the problem on geodesic bal...

In this paper, we prove the boundedness of all solutions for the equation x + n 2 x + φ(x) + g (x)q(t) = 0, where n ∈ N, q(t) = q(t + 2π), φ(x) and g(x) are bounded.