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In this paper, we study the existence of classical and gen- eralized solutions for nonlinear differential inclusions x′(t) ∈ F(t, x(t)) in Hilbert spaces in which the multifunction F on the right-hand side is hemicontinuous and satisfies the semimonotone condition or is condensing. Our existence results are obtained via the selection and fixed point methods by reducing the problem to an ordinary differential equation. We first prove the existence theorem in finite dimensional spaces and then we generalize the results to the infinite dimensional separable Hilbert spaces.
Then we apply the results to prove the existence of the mild solution for semilinear evolution inclusions. At last, we give an example to illustrate the results obtained in the paper.
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참고문헌 (25)
참고문헌 신청
A. Bressan / 1989 / On the qualitative theory of lower semicontinuous differential inclusions / J. Differential Equations 77 (2) : 379 ~ 391
A. Bressan / 1991 / Selections of Lipschitz multifunctions generating a continuous flow / Differential Integral Equations 4 (3) : 483 ~ 490
A. Bressan / 2009 / Classical solutions to differential inclusions with totaly dis-connected right-hand side / J. Differential Equations 246 (2) : 629 ~ 640
A. Cellina / 1970 / Multivalued differential equations and ordinary differential equations / SIAM J. Appl. Math 18 : 533 ~ 538
A. Cellina / 2005 / A view on differential inclusions / Rend. Semin. Mat. Univ. Politec. Torino 63 (3) : 197 ~ 209
A. Bressan / 1991 / Selections of Lipschitz multifunctions generating a continuous flow / Differential Integral Equations 4 (3) : 483 ~ 490
A. Bressan / 2009 / Classical solutions to differential inclusions with totaly dis-connected right-hand side / J. Differential Equations 246 (2) : 629 ~ 640
A. Cellina / 1970 / Multivalued differential equations and ordinary differential equations / SIAM J. Appl. Math 18 : 533 ~ 538
A. Cellina / 2005 / A view on differential inclusions / Rend. Semin. Mat. Univ. Politec. Torino 63 (3) : 197 ~ 209
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