Titile:
Existence Results for Coupled Elliptic Systems with Nonlinear Boundary Conditions
Abstract:
We investigate the existence of solutions to coupled systems of elliptic partial differential equations where nonlinearities appear both in the domain and on the boundary. Such problems arise naturally in applications including chemical reactions, biological processes, and ecological dynamics where interactions occur in boundary layers. Using the classical sub-supersolution method, we establish existence of minimal and maximal weak solutions under appropriate monotonicity conditions via iterative techniques. When monotonicity fails, we demonstrate existence through alternative approaches using Zorn's lemma combined with growth and boundedness assumptions. We illustrate our theoretical framework through concrete examples involving parameter-dependent systems with eigenvalue conditions.
Recording of some recent talks
Colloquium/Seminar
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Illinois Technological Institute Spring 2026
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Xavier University Louisiana Math Colloquium Spring 2026
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UT Martin Math Colloquium Spring 2026
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Iowa State University Math-Biology Seminar Fall 2025
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Northern Illinois University Math Colloquium Fall 2025
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Kenyon College Math Monday Fall 2025
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Wayne State University Math Colloquium Fall 2025
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Appalachian State University Math Colloquium Fall 2025
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Marshall University Math Colloquium Fall 2025
Invited Conference Talks
2026
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Fourth International Conference on Applications of Mathematics to Nonlinear Sciences (AMNS-2026)
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JMM 2026 (Two talks)
2025
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AMS Fall Central Sectional Meeting (Two talks)
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AMS Fall Western Sectional Meeting
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MAA MathFest
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International Conference on Difference Equations and Applications (ICDEA)
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MAA-SE Meeting
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Joint Mathematics Meetings (JMM)
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AMS Spring Central Sectional Meeting
2024
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14th AIMS Conference on Differential Equations (Two talks)
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Joint Mathematics Meetings (JMM)
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Southeastern Regional Conference on Differential Equations (SEARCDE) 2024
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International Conference on Differential Equations (ICDE)
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AMS Spring Central Sectional Meeting
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AMS Spring Southeastern Sectional Meeting
2023
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Joint Mathematics Meetings (JMM)
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Association for Women in Mathematics (AWM) Research Symposium (Two talks)
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13th AIMS Conference on Differential Equations (Two talks)
2022
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Joint Mathematics Meetings (JMM)
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Association for Women in Mathematics (AWM) Research Symposium
Contributed Conference Talks/Posters
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SIAM Great Lakes Conference 2025
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MAA-MathFest 2024 Early Career Poster Session (Poster)
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AMS Fall South Eastern Sectional 2022
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AWM Research Symposium Graduate Student Poster Session 2020 (Poster)
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SEARCDE 2019
