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Abstract This paper studies some quasilinear elliptic nonlocal equations involving Orlicz–Sobolev spaces. On the one hand, a new sub-supersolution theorem is proved via the pseudomonotone operator theory; on the other hand, using the obtained theorem, we present an existence result on the positive solutions of a singular elliptic nonlocal equation. Our work improves the results of some previous researches.

Abstract In this paper, using variational method, we study the existence of an infinite number of solutions (some are positive, some are negative, and others are sign-changing) for a non-homogeneous elliptic Kirchhoff equation with a nonlinear reaction term.

Abstract In this paper, we present a theorem for some impulsive boundary problems with derivative dependence by the upper and lower solutions method. Using the theorem obtained, we consider the existence of positive solutions of some class of singular impulsive boundary problems.

Abstract In this paper, we consider the singular Kirchhoff equation with two parameters {−a(∫Ω|∇u(x)|2dx)△u(x)+K(x)g(u)=λf(x,u)+μh(x)in Ω,u>0in Ω,u=0on ∂Ω. $$\textstyle\begin{cases} -a ( \int_{\varOmega}|\nabla u(x)|^{2}\,dx )\triangle u(x)+K(x)g(u)=\lambda f(x,u)+\mu h(x) \quad \mbox{in } \varOmega, \\ u>0 \quad \mbox{in } \varOmega, \\ u=0 \quad \mbox{on } \partial\varOmega. \end{cases} $$ By using the sub-supersolution method together with the comparison principle for elliptic equations, we obtain several existence and nonexistence theorems. Our works improve the results in the previous literature.

Abstract In this paper, we consider the generalized logistic equation with nonlocal reaction term −Δu=u(λ+b∫Ωurdx−f(u))in Ω,u>0 in Ω,u=0 on ∂Ω. $$ -\Delta u=u \biggl(\lambda +b \int_{\Omega }u^{r}\,dx-f(u) \biggr)\quad \text{in } \Omega,\qquad u>0 \quad \text{ in } \Omega,\qquad u=0 \quad \text{ on } \partial \Omega. $$ Using the bifurcation and sub-supersolution method, we obtain the non-existence, existence, and uniqueness of positive solutions for different parameters on the nonlocal terms. Our works about the nonlocal elliptic problem improve the results in the previous literature.

Abstract In Raman distributed temperature system, the key factor for performance improvement is noise suppression, which seriously affects the sensing distance and temperature accuracy. Therefore, we propose and experimentally demonstrate dynamic noise difference algorithm and wavelet transform modulus maximum (WTMM) to de-noising Raman anti-Stokes signal. Experimental results show that the sensing distance can increase from 3 km to 11.5 km and the temperature accuracy increases to 1.58 °C at the sensing distance of 10.4 km.

Positive solutions to the singular initial-boundary value problems x′′=−f(t, xt), 0