Elliptic PDEs with Concave and Convex Nonlinearities

Badajena, Arun Kumar (2022) Elliptic PDEs with Concave and Convex Nonlinearities. PhD thesis.

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Elliptic partial differential equations (PDEs) have applications in various fields of science and engineering such as conservation laws, reactiondiffusion problems, thin obstacle problem, phase transitions, crystal dislocation, soft thin films, elastic properties of fractal media and flow through fractal nonsmooth domains. It is also important in various fields of mathematics such as harmonic analysis, differential geometry and calculus of variations. In this thesis, the existence, multiplicity and regularity of solutions to some elliptic PDEs with concave and convex nonlinearities are considered. Existence of solutions are shown for elliptic problems defined on regular and fractal domains subject to different boundary conditions such as Dirichlet, Neumann or nonlinear boundary conditions. Some of the major techniques used in the thesis are: variational methods, weak convergence methods, Mountain pass theorem and its variants, method of subsuper solutions, critical point theory and the theory of monotone operators.

Item Type:Thesis (PhD)
Uncontrolled Keywords:Elliptic PDEs; Variational methods; Concave convex nonlinearities; Sierpinski gasket; Measure data; Monotone operators.
Subjects:Mathematics and Statistics > Analytical Mathematics
Mathematics and Statistics > Applied Mathematics
Divisions: Sciences > Department of Mathematics
ID Code:10453
Deposited By:IR Staff BPCL
Deposited On:04 Oct 2023 16:08
Last Modified:04 Oct 2023 16:09
Supervisor(s):Pradhan, Shesadev

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