We use an approximation scheme together with a variation of the fixed point theorem to show existence positive solution nonlocal boundary value problem. This problem has smooth bounded domain in R<sup>N</sup>, singular term, and combined nonlinearities. also study symmetric, monotonicity, asymptotic behavior solutions respect parameter involved

In this article, we consider a combination of local and nonlocal Laplace equation with singular nonlinearities. For such mixed problems, establish the existence at least one weak solution for parameter-dependent nonlinearity multiple solutions perturbed nonlinearity. Our argument is based on variational approximation approach.

We study optimal controls problems with final observation. The governing parabolic equations or systems involve superlinear nonlinearities and their solutions may blow up in finite time. Our proof of the existence, regularity and optimality conditions for an optimal pair is based on uniform a priori estimates for the approximating solutions. Our conditions on the growth of the nonlinearity are ...

We study a singular nonlinear ordinary differential equation on intervals [0, R) with R ≤ +∞, motivated by the Ginzburg–Landau models in superconductivity and Landau–de Gennes models in liquid crystals. We prove existence and uniqueness of positive solutions under general assumptions on the nonlinearity. Further uniqueness results for sign-changing solutions are obtained for a physically releva...

We show non-existence of solutions of the Cauchy problem in R for the nonlinear parabolic equation involving fractional diffusion ∂tu + (-∆) s φ(u) = 0, with 0 < s < 1 and very singular nonlinearities φ . More precisely, we prove that when φ(u) = −1/u with n > 0, or φ(u) = log u, and we take nonnegative L initial data, there is no (nonnegative) solution of the problem in any dimension N ≥ 2. We...

This paper studies the Lagrange stabilization of a class of nonlinear systems whose linear part has a singular system matrix and which have multiple periodic (in state) nonlinearities. Both state and output feedback Lagrange stabilization problems are considered. The paper develops a pseudo H∞ control theory to solve these stabilization problems. In a similar fashion to the Strict Bounded Real ...