We consider nonnegative solutions of the initial-boundary value problems in cone domains for the reaction-diffusion systems with inhomogeneous terms dependent on space coordinates and times. In our previous paper the conditions for the nonexistence of global solutions in time were shown. In this paper we show the condition of existence of global solutions in time.

Using a specially constructed cone and the fixed point index theory, this paper shows the existence of multiple positive solutions for a class of nonresonant singular boundary-value problem of second-order differential equations. The nonexistence of positive solution is also studied.

The existence or nonexistence of changes in meat consumption cycles is critical to meat industry. If the change is existent, there is a need to understand what motivates the change to identify the most appropriate response. Wavelet analysis is considered here as a promising technique that may lead to a better understanding of characteristic patterns and changes in the meat consumption cycles.

We consider the existence, the nonexistence, and the uniqueness of solutions of some special systems of nonlinear elliptic equations with boundary conditions. In a particular case, the system reduces to the homogeneous Dirichlet problem for the biharmonic equation ∆ 2 u = |u| p in a ball with p > 0.

Using the technique developed by F. John in 7], we study the existence and the nonexistence of global classical solutions to the Cauchy problem for @ 2 t u ? x u = jvj p ; @ 2 t v ? x v = juj q ; in R 3 x 0; +1.

when p = , |f (x,u)| ≤ c(|u|+ |u|q–),  < q≤ ∗ = N N– ,N ≥ , for the corresponding results onemay refer to Brézis [], Brézis and Nirenberg [], Bartsch andWillem [] and Capozzi, Fortunato and Palmieri []. Garcia and Alonso [] generalized Brézis, Nirenberg’s existence and nonexistence results to p-Laplace equation. Moreover, let us consider the following semilinear Schrödinger equation:

In this paper, a fourth-order nonlinear p-Laplacian difference equation is considered. Using the critical point theory, we establish various sets of sufficient conditions of the nonexistence and existence of solutions for Neumann boundary value problem and give some new results. The existing results are generalized and significantly complemented.

This paper is devoted to the study of existence and nonexistence positive solutions for a second-order m-point eigenvalue impulsive boundary value problem. We use fixed point theorems on cones in order achieve our results.

We obtain upper and lower estimates for positive solutions of a third-order three-point boundary-value problem. Sufficient conditions for the existence and nonexistence of positive solutions for the problem are also obtained. Then to illustrate our results, we include an example.

In this work, we study a plate equation with time delay in the velocity, frictional damping, and logarithmic source term. Firstly, obtain local global existence of solutions by Sobolev inequality Faedo-Galerkin method. Moreover, prove stability nonexistence results perturbed energy potential well methods.