109 research outputs found
On (,)-Laplace Schrödinger equations with Stein-Weiss convolution parts in Rn
No full textBy using the mountain pass theorem, this article deals with the existence of positive ground state solutions to a class of (,)-Laplace Schrödinger equations with Stein-Weiss reaction under critical exponential growth in the sense of the Moser–Trudinger inequality in the whole Rn.TU Berlin, Open-Access-Mittel – 202
On singularly perturbed (p, N)-Laplace Schrödinger equation with logarithmic nonlinearity
No full textThis article focuses on the study of the existence, multiplicity and concentration behavior of ground states as well as the qualitative aspects of positive solutions for a (p, N)-Laplace Schrödinger equation with logarithmic nonlinearity and critical exponential nonlinearity in the sense of Trudinger-Moser in the whole Euclidean space ℝ . Through the use of smooth variational methods, penalization techniques, and the application of the Lusternik–Schnirelmann category theory, we establish a connection between the number of positive solutions and the topological properties of a set in which the potential function achieves its minimum values.TU Berlin, Open-Access-Mittel – 202
Degenerate Schr{\"o}dinger-Kirchhoff -Laplacian problem With singular Trudinger-Moser nonlinearity in
No full textIn this paper, we deal with the existence of nontrivial nonnegative solutions
for a -Laplacian Schr{\"o}dinger-Kirchhoff problem in
with singular exponential nonlinearity. The main features of the paper are the
growth of the elliptic operators, the double lack of compactness, and
the fact that the Kirchhoff function is of degenerate type. To establish the
existence results, we use the mountain pass theorem, the Ekeland variational
principle, the singular Trudinger-Moser inequality, and a completely new
Br\'ezis-Lieb type lemma for singular exponential nonlinearity
On singularly perturbed -Laplace Schr\"{o}dinger equation with logarithmic nonlinearity
No full textThis article focuses on the study of the existence, multiplicity and
concentration behavior of ground states as well as the qualitative aspects of
positive solutions for a -Laplace Schr\"{o}dinger equation with
logarithmic nonlinearity and critical exponential nonlinearity in the sense of
Trudinger-Moser in the whole Euclidean space . Through the use of
smooth variational methods, penalization techniques, and the application of the
Lusternik-Schnirelmann category theory, we establish a connection between the
number of positive solutions and the topological properties of the set in which
the potential function achieves its minimum values.Comment: 51 page
Dilemmas of Trishanku
No full textThis is an interesting account of our contemporary society that is plagued with several contradictions depicted in the puranic mould. Taking the puranic character of how Trishanku was hanging in the air belonging neither here nor there, the author narrated important events and socio-economic processes that keep artisans of certain castes as displaced persons while upper castes make suitable adjustments for upward mobility. The author has identified the Three Cs, corruption, casteism and communalism as disturbing trends that tear apart present-day Indian society. He has aspired that the three Ds, development, democracy and diversity might tackle them. Using Emic and Etic approaches, the author explains his participant observations for the benefit of the perceptible reader. Around 300 pages book is reasonably priced
Flip Learning experiments. An introductory course in A.I
No full textActive learning with Flip learning techniques are described in an active learning course in introductory A.I , taught at IIT Madras Computer Sciences Department, by the author in collaboration with Dr Deepak Khemani. In a methodology of flip learning and inverting the classroom, a system of surprise quizzes as more than an assessment, but a self exploratory flip learning pedagogy, with open ended deadlines.
The author describes a flip learning methodology, with preparatory reading and future reading summaries, as part of an open evaluation as part of the course instruction, combined with lectures, eliminating examinations, quizzes and traditional assessment techniques.
As a novel approach, the grading is modified to award original contributions, more than a good understanding of the subject matter, with a viva voce for a grading poorer than a B, inspired by Prof Josua Chover of UW Madison.
This active learning methodology builds on the methods practiced by Prof V Balakrishnan of the Physics department, IIT Madras, Prof Deepak Khemani of Computer Sciences , IIT Madras and Prof Joshua Chover of the Mathematics Department, UW Madison.
Keywords: Active Learning, Flip Learning, Undergrad instruction, Creative thinking, critical thinkin
Numerical modeling and performance analysis of zinc oxide (ZnO) thin-film based gas sensor
No full textOn the study of -Laplace Choquard equations with critical Trudinger-Moser nonlinearity in
No full textThis paper deals with the existence and multiplicity of nontrivial solutions for -Laplace equations with the Stein-Weiss reaction under critical exponential nonlinearity in the Heisenberg group . In addition, a weight function and two positive parameters have also been included in the nonlinearity. The developed analysis is significantly influenced by these two parameters. Further, the mountain pass theorem, the Ekeland variational principle, the Trudinger-Moser inequality, the doubly weighted Hardy-Littlewood-Sobolev inequality and a completely new Brézis-Lieb type lemma for Choquard nonlinearity play key roles in our proofs.25 page
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