A nonlinear boundary value problem involving the p-biharmonic operator is investigated, where p > 1. It describes various problems in the theory of elasticity, e.g., the shape of an elastic beam where the bending moment depends on the curvature as a power function with exponent p − 1. We prove existence of solutions satisfying a quite general boundary condition that incorporates many particular boundary conditions which are frequently considered in the literature.
In this paper we study the existence and multiplicity of nontrivial solutions for a boundary value problem associated with a semilinear sixth-order ordinary differential equation arising in the study of spatial patterns. Our treatment is based on variational tools, including two Brezis-Nirenberg's linking theorems.
We study theAmerican option pricing linear complementarity problem (LCP), transformed on finite interval as it is initially defined on semi-infinite real axis. We aim to validate this transformation, investigating the well-posedness of the resulting problem in weighted Sobolev spaces. The monotonic penalty method reformulates the LCP as a semi-linear partial differential equation (PDE) and our analysis of the penalized problem results in uniform convergence estimates. The resulting PDE is further discretized by a fitted finite volume method since the transformed partial differential operator degenerates on the boundary. We show solvability of the semi-discrete and fully discrete problems. The Brennan-Schwarz algorithm is also presented for comparison of the numerical experiments, given in support to our theoretical considerations.
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