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We give a unified approach to study the existence of multiple positive solutions of nonlinear differential inclusions of the form −u′′(t)∈F(t,u(t)),a.e.t∈(0,1),$$\begin{equation*}\hskip7pc -u^{\prime \prime }(t)\in F(t,u(t)),\; \text{a.e.} \; t \in (0,1), \end{equation*}$$subject to various nonlocal boundary conditions. We study these problems via a perturbed integral inclusion of the form u(t)∈Bu(t)+∫01k(t,s)F(s,u(s))ds$ u(t)\in Bu(t) +\int _{0}^{1}k(t,s)F(s,u(s))\,ds$. [ABSTRACT FROM AUTHOR]

We study the existence and multiplicity of positive radial solutions for a coupled elliptic system in exterior domains where the nonlinearities depend on the gradients and the boundary conditions are nonlocal. We use a new cone to establish the existence of solutions by means of fixed point index theory. [ABSTRACT FROM AUTHOR]

We provide new results on the existence, nonexistence, and multiplicity of nonnegative radial solutions for semilinear elliptic systems with Neumann boundary conditions on an annulus. Our approach is topological and relies on the classical fixed‐point index. We present an example to illustrate our theory. [ABSTRACT FROM AUTHOR]

Using the theory of fixed point index, we discuss existence, non-existence, localization and multiplicity of positive solutions for a $(p_{1},p_{2})$-Laplacian system with nonlinear Robin and/or Dirichlet type boundary conditions. We give an example to illustrate our theory. [ABSTRACT FROM AUTHOR]

We study existence and multiplicity of positive radial solutions for a semipositone coupled elliptic system in exterior domains where the nonlinearities depend on the gradients and the Neumann boundary conditions are nonlocal. We use a nonstandard cone to establish existence of multiple solutions by means of fixed point index theory. [ABSTRACT FROM AUTHOR]

In this paper new criteria are established for the existence of positive radial solutions of a semilinear elliptic system depending on the gradient. These criteria are determined by some relationships between the upper and lower bounds on suitable strips of R n of the nonlinearities of the system and the principal characteristic values of some associated linear Hammerstein integral operators. Moreover, using smoothing tools, the totality of the involved cone is established. [ABSTRACT FROM AUTHOR]