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Positive solutions of nonlinear elliptic systems

100%

Dalmasso R.

Annales Polonici Mathematici

1993

tom 58

nr 2

201-212

We study the existence and nonexistence of positive solutions of nonlinear elliptic systems in an annulus with Dirichlet boundary conditions. In particular, $L^∞$ a priori bounds are obtained. We also study a general multiple linear eigenvalue problem on a bounded domain.

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Systems of differential inclusions in the absence of maximum principles and growth conditions

75%

Tisdell C.

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

2006

tom 26

nr 1

129-141

This article investigates the existence of solutions to second-order boundary value problems (BVPs) for systems of ordinary differential inclusions. The boundary conditions may involve two or more points. Some new inequalities are presented that guarantee a priori bounds on solutions to the differential inclusion under consideration. These a priori bound results are then applied, in conjunction with appropriate topological methods, to prove some new existence theorems for solutions to systems of BVPs for differential inclusions. The new conditions allow the treatment of systems of BVPs in the absence of maximum principles and growth conditions. The results are also new for differential equations involving Carathéodory or even continuous right-hand sides.

The existence of solution for boundary value problems for differential equations with deviating arguments and p-Laplacian

75%

Liu B., Yu J.

Annales Polonici Mathematici

2000

tom 75

nr 3

271-280

We consider a boundary value problem for a differential equation with deviating arguments and p-Laplacian: $-(ϕ_{p}(x'))' + d/dt grad F(x) + g(t,x(t),x(δ(t))$, x'(t), x'(τ(t))) = 0, t ∈ [0,1]; $x(t)=\underline{φ}(t),$ t ≤ 0; $x(t) = \overline{φ}(t)$, t ≥ 1. An existence result is obtained with the help of the Leray-Schauder degree theory, with no restriction on the damping forces d/dt grad F(x).

Ograniczanie wyników

2 Annales Polonici Mathematici

1 Discussiones Mathematicae, Differential Inclusions, Control and Optimization

1 Dalmasso R.

1 Liu B.

1 Tisdell C.

1 Yu J.

1 2006

1 2000

1 1993

Wyniki wyszukiwania

Positive solutions of nonlinear elliptic systems

Systems of differential inclusions in the absence of maximum principles and growth conditions

The existence of solution for boundary value problems for differential equations with deviating arguments and p-Laplacian