This paper investigates the existence and asymptotic behavior of solutions for weighted p t Laplacian integro-differential system with multipoint and integral boundary value condition in half line. When the nonlinearity term f satisfies subp− − 1 growth condition or general growth condition, we give the existence of solutions via Leray-Schauder degree. Moreover, the existence of nonnegative sol...

A semilinear elliptic boundary-value problem on bounded multiconnected domains is studied. The authors prove that under suitable conditions, the problem may have no solutions in certain cases and many have one or two nonnegative solutions in some other cases. The radial solutions were also studied in annular domains.

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.

In this note we summarize our recent results on nonnegative solutions of nonlinear elliptic equations on reflectionally symmetric domains. We discuss symmetry properties of such solutions, the structure of their nodal set, and the existence and multiplicity of solutions with a nontrivial nodal set.

In this paper we consider fully nonlinear elliptic operators of the form F (x, u,Du,D2u). Our aim is to prove that, under suitable assumptions on F , the only nonnegative viscosity super-solution u of F (x, u,Du,D2u) = 0 in an unbounded domain Ω is u ≡ 0. We show that this uniqueness result holds for the class of nonnegative super-solutions u satisfying inf x∈Ω u(x) + 1 dist(x, ∂Ω) = 0, and the...

We investigate vanishing properties of nonnegative solutions of anisotropic elliptic and parabolic equations. We describe the optimal vanishing sets, and we establish strong maximum principles.