Solutions of nonlinear evolution inclusions

Bian, W.; Webb, J. R. L.

doi:10.1016/s0362-546x(98)00082-0

Cited by 6 publications

(6 citation statements)

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“…It is known that, under (H2)-(H4), A is a well-defined bounded mapping from L p (V ) to L q (V * ) with closed convex values. Moreover, in [3], the authors proved the following results which remains valid if we replace the general triple by a Hilbert space one.…”

Section: Preliminariesmentioning

confidence: 92%

“…Problems (1.1) and (1.2) allow many special cases that have been studied already. When B is the identity operator on V , (1.1) is the problem considered by the Bian and Webb in [3] (where V can be a reflexive Banach space). When A(t, x) ≡ A(x) and A is a maximal monotone mapping, (1.1) is studied by Barbu and Favini in [2].…”

Section: Introductionmentioning

confidence: 99%

“…and, from this property, the continuity result for (1.1) and the solvability for (1.2) can be derived which are not given in [1], [2] or [3].…”

Section: Introductionmentioning

confidence: 99%

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Solutions of implicit evolution inclusions with pseudo-monotone mappings

Bian¹

2000

TMNA

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Existence results are given for the implicit evolution inclusions (Bx(t)) + A(t, x(t)) f (t) and (Bx(t)) + A(t, x(t)) − G(t, x(t)) f (t) with B a bounded linear operator, A(t, • ) a bounded, coercive and pseudo-monotone set-valued mapping and G a set-valued mapping of nonmonotone type. Continuity of the solution set of first inclusion with respect to f is also obtained which is used to solve the second inclusion.

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Section: Preliminariesmentioning

confidence: 92%

Section: Introductionmentioning

confidence: 99%

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Solutions of implicit evolution inclusions with pseudo-monotone mappings

Bian¹

2000

TMNA

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“…and Bian [7,8] considered the solution of the evolution inclusion problem du dt + B t, u(t) 0, here B(t, ·) : V → V * is a pseudo-monotone operator. He gave an existence result to this problem and generalized the results in [3,6,8,13].…”

Section: U(t) Du Dtmentioning

confidence: 99%

Solutions of nonlinear evolution inclusions

2006

Journal of Mathematical Analysis and Applications

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In this paper, the solution of the nonlinear evolution inclusion problem of the form u (t) + B(t, u(t)) f (t) is studied. In this problem, the operators are of type (M) or type (S + ), which are different from those of pseudo-monotone operators that had been studied by many authors. At the same time, we study the perturbation problem. In fact, many kinds of evolution equations can be generalized by this problem. The former results are improved and generalized by our conclusions, and we will give more applications.  2005 Elsevier Inc. All rights reserved.

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“…This means that the hypotheses made on the operator in [7] are strong enough so that the result on existence of solutions to the evolution inclusion in [7] is a consequence of a theorem of Bian and Webb [3].…”

Section: Introductionmentioning

confidence: 99%