Solvability of inclusions involving perturbations of positively homogeneous maximal monotone operators

Electronic Journal of Differential Equations

article

Dhruba R. Adhikari¹  Ashok Aryal²  Ghanshyam Bhatt³  Ishwari J. Kunwar⁴  Rajan Puri⁵  Min Ranabhat⁶ 

[1] Department of Mathematics Kennesaw State University Marietta;Mathematics Department Minnesota State University Moorhead Moorhead;Department of Mathematical Sciences Tennessee State University Nashville;Department of Mathematics and Computer Science Fort Valley State University Fort Valley;Department of Mathematics Wake Forest University Winston-Salem;Department of Mathematical Sciences University of Delaware EWG 315

关键词: Topological degree theory;    operators of type;    monotone operator;    duality mapping;    Yosida approximant.;   

DOI  :  10.58997/ejde.2022.63

学科分类：数学（综合）

来源: Texas State University

【 摘 要 】

Letbe a real reflexive Banach space andbe its dual space. Letandbe open subsets of such that ,, and is bounded. Letbe a densely defined linear maximal monotone operator,be a maximal monotone and positively homogeneous operator of degree,be a bounded demicontinuous operator of typewith respect to, and be a compact and upper-semicontinuous operator whose values are closed and convex sets in. We first takeand establish the existence of nonzero solutions ofin the set. Secondly, we assume thatis bounded and establish the existence of nonzero solutions ofin. We remove the restrictionsforand forfrom such existing results in the literature. We also present applications to elliptic and parabolic partial differential equations in general divergence form satisfying Dirichlet boundary conditions.

【 授权许可】

CC BY