Nonlinear differential equations with nonlocal conditions in Banach spaces

Multivalued evolution equations with nonlocal initial conditions in Banach spaces

“…To accomplish this, we reason as follows. (A comparable argument was independently used by Xue [28], in a different context. )…”

“…Results on fully nonlinear abstract nonlocal Cauchy problem have been obtained in [2], [3], [4]. While we were concluding the writing up of this article, Xue's very recent work [28] has been brought to our attention. These papers are primarily concerned with equations governed by accretive operators and single-valued perturbations.…”

“…By(H g ) , it is easily verified that L is one-to-one and onto, and that L −1 is continuous on X 0 , see [28], Lemma 2.5. Accordingly, we write…”

Second order evolution equations with nonlocal conditions

“…the study of evolution initial value problems with nonlocal conditions is of signi cance since they have applications in problems in physics and other areas of applied mathematics. Several authors have investigated the problem of nonlocal initial conditions for di erent classes of abstract di erential equations in Banach spaces, for example, we refer the reader to [15][16][17][18][19][20][21] and the references therein.…”

Monotone iterative method for abstract impulsive integro-differential equations with nonlocal conditions in Banach spaces

“…They studied and obtained the existence and uniqueness of mild solutions for nonlocal differential equations without impulsive conditions. Since it has been demonstrated that the nonlocal problems have better effects in applications than the traditional Cauchy problems, differential equations with nonlocal conditions have been studied by many authors and some basic results on nonlocal problems have been obtained, see [6], [7], [8], [13], [17], [18], [21], [25], [31], [33], [34], [36], [40], [41], [42], and the references therein for more comments and citations. In 2009, Liang et al [32] combined the impulsive conditions and the nonlocal conditions, and investigated the nonlocal problem of impulsive evolution equations in Banach spaces.…”