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Superlinear Elliptic Equations and Systems [PDF]
, 2008 In this article we survey some recent results on superlinear elliptic equations and systems. A particular focus will be the borderline situations of so-called critical growth. In the existence theorems, we will use mostly variational methods, that is we look for critical points of functionals associated to the equations and systems.
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Advanced Functional Materials, EarlyView.Nanosecond pulse laser texturing yields superhydrophobic and superhydrophilic AA2024 surfaces. Salt‐spray tests show that periodic superhydrophobic patterns suppress pitting, whereas superhydrophilic textures enhance it, linking laser‐induced morphology, wettability, and oxide chemistry to corrosion resistance.
Lis Geraldine Zschach +8 more
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Electronic Journal of Differential Equations, 2004 We prove a critical-point result which provides conditions for the existence of infinitely many critical points of a strongly indefinite functional with perturbed symmetries.
Monica Clapp +2 more
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On critical semilinear elliptic systems
Advances in Differential Equations, 2001 The goal of the present paper is to study the existence of solutions of the semilinear elliptic system \[ \begin{gathered} -\Delta u+ u= |v|^{q-1} v+ g(x,v)\quad\text{in }\mathbb{R}^n,\\ -\Delta v+ v= |u|^{p-1} u+ f(x,u)\quad\text{in }\mathbb{R}^N,\\ u(x)\to 0\text{ and }v(x)\to 0\quad \text{as }|x|\to \infty,\end{gathered}\tag{1} \] where \({1\over p ...
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Shaping of Biohybrid Functional Living Materials
Advanced Functional Materials, EarlyView.This work demonstrates a strategy for shaping living mycelium into functional materials by directing its natural growth. Nanoparticles armor hyphae, micron‐scale particles entangle within the network, and printed hydrogel architectures steer expansion, creating defined geometries.
Sarah Schyck +3 more
wiley +1 more source
Multiplicity of Positive Solutions for Semilinear Elliptic Systems
Abstract and Applied Analysis, 2013 We study the effect of the coefficient of the critical nonlinearity on the number of positive solutions for semilinear elliptic systems. Under suitable assumptions for , , and , we should prove that for sufficiently small , there are at least positive ...
Tsing-San Hsu
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Doubly Periodic Meromorphic Solutions of Autonomous Nonlinear Differential Equations
Моделирование и анализ информационных систем, 2014 The problem of constructing and classifying elliptic solutions of nonlinear differential equations is studied. An effective method enabling one to find an elliptic solution of an autonomous nonlinear ordinary differential equation is described.
M. V. Demina, N. A. Kudryashov
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Advanced Functional Materials, EarlyView.Reprogrammable multi‐material smart textiles knitted from liquid crystal elastomer fibers undergo 2D and 3D deformation under thermal and photo stimuli. Circularly knitted tubular structures reversibly contract in radial and axial directions, enabling autonomous climbing, liquid release, and micro pumping.
Xue Wan +8 more
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Advanced Functional Materials, EarlyView.Terminal domains of recombinant collagen‐like silk regulate hierarchical self‐assembly across molecular and material scales. We show that terminal domains of collagen‐like silk enhance triple‐helix stability and drive liquid–liquid phase separation, enabling reversible formation of fibers and self‐healing films.
Mengjie Shen +5 more
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Existence of positive solutions for some nonlinear elliptic systems on the half space
Electronic Journal of Differential Equations, 2011 We prove some existence of positive solutions to the semilinear elliptic system $$displaylines{ Delta u =lambda p(x)g(v)cr Delta v =mu q(x)f(u) }$$ in the half space ${mathbb{R}}^n_+$, $ngeq 2$, subject to some Dirichlet conditions, where $lambda$
Noureddine Zeddini
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