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The main purpose of this paper is to study the existence of least energy sign-changing solutions for Logarithmic weighted $(N,p)$-Laplacian problem in the unit ball $B$ of $\mathbb{R}^{N},$ $N>2$. The non-linearity of the equation is assumed to have...
We systematically study a numerical procedure that reveals the asymptotically self-similar dynamics of solutions of partial differential equations (PDEs). This procedure, based on the renormalization group (RG) theory for PDEs, appeared initially in...
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The proof of a result of J. J. Nieto [3] appeared in "Acta Math, Hung". (1992) concerning the positive solutions of nonlinear problems at resonance is corrected and improved....
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Concentrated aqueous solutions of the protein lysozyme undergo a liquid solid transition upon a temperature quench into the unstable spinodal region below a characteristic arrest temperature of Tf=15C. We use video microscopy and ultra-small angle...
Harbour Solutions is a Canadian public infrastructure project in Halifax, Nova Scotia. The CAD $333 million project comprised the construction of three
A semilinear reaction-diffusion two-point boundary value problem, whose second-order derivative is multiplied by a small positive parameter $\eps^2$, is considered. It can have multiple solutions. An asymptotic expansion is constructed for a solution...
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While the history of machine learning so far largely encompasses a series of problems posed by researchers and algorithms that learn their solutions, an important question is whether the problems themselves can be generated by the algorithm at the sa...