In this note, we study the existence and multiplicity of solutions, strictly positive or nonnegative having a dead core (where the solution vanishes) of several nonlinear problems of eigenvalue type. 2000 Mathematics Subject Classification: 35J60, 35B52.

This article studies the existence of nonnegative solutions for a boundary value problem (BVP) of nonlinear fractional differential equations. Some new existence results are obtained by applying Kranoselskii‘s fixed–point theorem in a cone. First we prove the existence of solutions of an auxiliary BVP formulated by truncating the response function. Then the Arzela–Ascoli theorem is used to take...

Existence of nonnegative solutions are established for the periodic problem y = f(t, y) a.e. on [0, T ], y(0) = y(T ). Here the nonlinearity f satisfies a Landesman Lazer type condition.

We study the uniqueness and stability of nonnegative solutions for classes of nonlinear elliptic Dirichlet problems on a ball, when the nonlinearity is monotone, negative at the origin, and either concave or convex.

For a coagulation equation with Becker-Döring type interactions and time-independent monomer input we study the detailed long-time behaviour of nonnegative solutions and prove the convergence to a selfsimilar function.

In this paper, a quasilinear elliptic system is investigated, which involves concave-convex nonlinearities and nonlinear boundary condition. By Nehari manifold, fibering method and analytic techniques, the existence of multiple nontrivial nonnegative solutions to this equation is verified.

We consider a large class of differential inequalities on complete connected Riemannian manifolds, and provide a sufficient condition in terms of volume growth for the uniqueness of nonnegative solutions to the differential inequalities.

Conditions are given on the nonnegative data «jc) and g{x, t) such that solutions of the pseudoparabolic inequality P[u] =» (L I)u, + Lu < 0 in Dx (0, t)

In this paper, we study the existence of multiple solutions of nonlocal boundary value problems for fractional differential equations with integral boundary conditions on the half-line. Applying the fixed point theory and the upper and lower solutions method, some new results on the existence of at least three nonnegative solutions are obtained. An example is presented to illustrate the applica...

This paper investigates the problem of decentralized model reference adaptive control (MRAC) for a class of large scale systems with time varying delays in interconnected terms and state and input delays. The upper bounds of the interconnection terms are considered to be unknown. Time varying delays in the nonlinear interconnection terms are bounded and nonnegative continuous functions and thei...