Search results for "robin boundary condition"
showing 4 items of 24 documents
A Sub-Supersolution Approach for Robin Boundary Value Problems with Full Gradient Dependence
2020
The paper investigates a nonlinear elliptic problem with a Robin boundary condition, which exhibits a convection term with full dependence on the solution and its gradient. A sub- supersolution approach is developed for this type of problems. The main result establishes the existence of a solution enclosed in the ordered interval formed by a sub-supersolution. The result is applied to find positive solutions.
A Fixed Domain Approach in Shape Optimization Problems with Neumann Boundary Conditions
2008
Fixed domain methods have well-known advantages in the solution of variable domain problems, but are mainly applied in the case of Dirichlet boundary conditions. This paper examines a way to extend this class of methods to the more difficult case of Neumann boundary conditions.
A posteriori error estimates for time-dependent reaction-diffusion problems based on the Payne-Weinberger inequality
2015
We consider evolutionary reaction-diffusion problem with mixed Dirichlet--Robin boundary conditions. For this class of problems, we derive two-sided estimates of the distance between any function in the admissible energy space and exact solution of the problem. The estimates (majorants and minorants) are explicitly computable and do not contain unknown functions or constants. Moreover, it is proved that the estimates are equivalent to the energy norm of the deviation from the exact solution.
Positive solutions for nonlinear Robin problems
2017
We consider a parametric Robin problem driven by the p-Laplacian with an indefinite potential and with a superlinear reaction term which does not satisfy the Ambrosetti-Rabinowitz condition. We look for positive solutions. We prove a bifurcation-type theorem describing the nonexistence, existence and multiplicity of positive solutions as the parameter varies. We also show the existence of a minimal positive solution $\tilde{u}_\lambda$ and establish the monotonicity and continuity of the map $\lambda\to \tilde{u}_\lambda$.