A multiplicity result for quasilinear problems with convex and concave nonlinearities and nonlinear boundary conditions inunbounded domains.
A subsolution-supersolution method for quasilinear systems.
Existence and uniqueness results of positive solutions for nonvariational quasilinear elliptic systems.
Evolution inclusions of the subdifferential type depending on a parameter.
An existence result for nonlinear evolution equations of second order
In this paper we consider a second order differential equation involving the difference of two monotone operators. Using an auxiliary equation, a priori bounds and a compactness argument we show that the differential equation has a local solution. An example is also presented in detail.
On Neumann boundary value problems for elliptic equations
We provide two existence results for the nonlinear Neumann problem ⎧-div(a(x)∇u(x)) = f(x,u) in Ω ⎨ ⎩∂u/∂n = 0 on ∂Ω, where Ω is a smooth bounded domain in , a is a weight function and f a nonlinear perturbation. Our approach is variational in character.
Pseudomonotonicity and nonlinear hyperbolic equations
In this paper we consider a nonlinear hyperbolic boundary value problem. We show that this problem admits weak solutions by using a lifting result for pseudomonotone operators and a surjectivity result concerning coercive and monotone operators.
A fibering method approach to a system of quasilinear equations with nonlinear boundary conditions
We provide an existence result for a system of quasilinear equations subject to nonlinear boundary conditions on a bounded domain by using the fibering method.
Correction on “The properties of the Aumann integral with applications to differential inclusions and control systems”
A -Laplacian system with resonance and nonlinear boundary conditions on an unbounded domain
We study a nonlinear elliptic system with resonance part and nonlinear boundary conditions on an unbounded domain. Our approach is variational and is based on the well known Landesman-Laser type conditions.
Multiplicity of positive solutions for some quasilinear Dirichlet problems on bounded domains in
We show that, under appropriate structure conditions, the quasilinear Dirichlet problem where is a bounded domain in , , admits two positive solutions , in such that in , while is a local minimizer of the associated Euler-Lagrange functional.
Periodic solutions for nonlinear Volterra integrodifferential equations in Banach spaces
In this paper we examine periodic integrodifferential equations in Banach spaces. When the cone is regular, we prove two existence theorems for the extremal solutions in the order interval determined by an upper and a lower solution. Both theorems use only the order structure of the problem and no compactness condition is assumed. In the last section we ask the cone to be only normal but we impose a compactness condition using the ball measure of noncompactness. We obtain the extremal solutions...
Evolution inclusions of the subdifferential type depending on a parameter
In this paper we study evolution inclusions generated by time dependent convex subdifferentials, with the orientor field depending on a parameter. Under reasonable hypotheses on the data, we show that the solution set is both Vietoris and Hausdorff metric continuous in . Using these results, we study the variational stability of a class of nonlinear parabolic optimal control problems.
Periodic solutions for nonlinear evolution inclusions
In this paper we prove the existence of periodic solutions for a class of nonlinear evolution inclusions defined in an evolution triple of spaces and driven by a demicontinuous pseudomonotone coercive operator and an upper semicontinuous multivalued perturbation defined on with values in . Our proof is based on a known result about the surjectivity of the sum of two operators of monotone type and on the fact that the property of pseudomonotonicity is lifted to the Nemitsky operator, which we...
On the properties of the Aumann integral with applications to differential inclusions and control systems
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