Solvability of inclusions involving perturbations of positively homogeneous maximal monotone operators
| dc.contributor.author | Adhikari, Dhruba R. | |
| dc.contributor.author | Aryal, Ashok | |
| dc.contributor.author | Bhatt, Ghanshyam | |
| dc.contributor.author | Kunwar, Ishwari | |
| dc.contributor.author | Puri, Rajan | |
| dc.contributor.author | Ranabhat, Min | |
| dc.date.accessioned | 2023-04-25T19:57:19Z | |
| dc.date.available | 2023-04-25T19:57:19Z | |
| dc.date.issued | 2022-08-30 | |
| dc.description.abstract | Let X be a real reflexive Banach and X* be its dual space. Let G1 and G2 be open subsets of X* such that Ḡ2 ⊂ G1, 0 ∈ G2, and G1 is bounded. Let L : X ⊃ D(L) → X* be a densely defined linear maximal monotone operator, A : X ⊃ D(A) → 2X* be a maximal monotone and positively homogeneous operator of degree γ > 0, C : X ⊃ D(C) → X* be a bounded demicontinuous operator of type (S+) with respect to D(L), and T : Ḡ1 → 2X* be a compact and upper-semicontinuous operator whose values are closed and convex sets in X*. We first take L = 0 and establish the existence of nonzero solutions of Ax + Cx + Tx ∋ 0 in the set G1 \ G2. Secondly, we assume that A is bounded and establish the existence of nonzero solutions of Lx + Ax + Cx ∋ 0 in G1 \ G2. We remove the restrictions γ ∈ (0, 1] for Ax + Cx + Tx ∋ 0 and γ = 1 for Lx + Ax + Cx ∋ 0 from such existing results in the literature. We also present applications to elliptic and parabolic partial differential equations in general divergence from satisfying Dirichlet boundary conditions. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 25 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Adhikari, D. R., Aryal, A., Bhatt, G., Kunwar, I. J., Puri, R., & Ranabhat, M. (2022). Solvability of inclusions involving perturbations of positively homogeneous maximal monotone operators. Electronic Journal of Differential Equations, 2022(63), pp. 1-25. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/16653 | |
| 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.subject | Topological degree theory | |
| dc.subject | Operators of type (S+) | |
| dc.subject | Monotone operator | |
| dc.subject | Duality mapping | |
| dc.subject | Yosida approximant | |
| dc.title | Solvability of inclusions involving perturbations of positively homogeneous maximal monotone operators | |
| dc.type | Article |