Nontrivial solutions of inclusions involving perturbed maximal monotone operators
| dc.contributor.author | Adhikari, Dhruba R. | |
| dc.date.accessioned | 2022-06-03T17:06:40Z | |
| dc.date.available | 2022-06-03T17:06:40Z | |
| dc.date.issued | 2017-06-25 | |
| dc.description.abstract | Let X be a real reflexive Banach space and X* its dual space. Let L : X ⊃ D(L) → X* be a densely defined linear maximal monotone operator, and T : X ⊃ D(T) → 2X*, 0 ∈ D(T) and 0 ∈ T(0), be strongly quasibounded maximal monotone and positively homogeneous of degree 1. Also, let C : X ⊃ D(C) → X* be bounded, demicontinuous and of type (S+) w.r.t. to D(L). The existence of nonzero solutions of Lx + Tx + Cx ∋ 0 is established in the set G1 \ G2, where G2 ⊂ G1 with Ḡ2 ⊂ G1, G1, G2 are open sets in X, 0 ∈ G2, and G1 is bounded. In the special case when L = 0, a mapping G : Ḡ1 → X* of class (P) introduced by Hu and Papageorgiou is also incorporated and the existence of nonzero solutions of Tx + Cx + Gx ∋ 0, where T is only maximal monotone and positively homogeneous of degree α ∈ (0, 1], is obtained. Applications to elliptic partial differential equations involving p-Laplacian with p ∈ (1, 2] and time-dependent parabolic partial differential equations on cylindrical domains are presented. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 21 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Adhikari, D. R. (2017). Nontrivial solutions of inclusions involving perturbed maximal monotone operators. Electronic Journal of Differential Equations, 2017(151), pp. 1-21. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/15844 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2017, San Marcos, Texas: Texas State University and University of North Texas. | |
| dc.subject | Strong quasiboundedness | |
| dc.subject | Browder and Skrypnik degree theories | |
| dc.subject | Maximal monotone operator | |
| dc.subject | Bounded demicontinuous operator of type (S+) | |
| dc.title | Nontrivial solutions of inclusions involving perturbed maximal monotone operators | |
| dc.type | Article |