scholarly journals A Sub-Supersolution Approach for Robin Boundary Value Problems with Full Gradient Dependence

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 658 ◽  
Author(s):  
Dumitru Motreanu ◽  
Angela Sciammetta ◽  
Elisabetta Tornatore
Keyword(s):  
Boundary Condition ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Elliptic Problem ◽  
Robin Boundary Condition ◽  
Convection Term ◽  
Nonlinear Elliptic Problem ◽  
Existence Of A Solution ◽  
Nonlinear Elliptic ◽  
Robin Boundary

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.

Semilinear Robin problems resonant at both zero and infinity

2018 ◽  
Vol 30 (1) ◽  
pp. 237-251
Author(s):  
Nikolaos S. Papageorgiou ◽  
Vicenţiu D. Rădulescu
Keyword(s):  
Boundary Condition ◽  
Variational Methods ◽  
Elliptic Problem ◽  
Robin Boundary Condition ◽  
Critical Groups ◽  
Smooth Solutions ◽  
Reaction Term ◽  
Semilinear Elliptic Problem ◽  
Semilinear Elliptic ◽  
Robin Boundary

Abstract We consider a semilinear elliptic problem, driven by the Laplacian with Robin boundary condition. We consider a reaction term which is resonant at {\pm\infty} and at 0. Using variational methods and critical groups, we show that under resonance conditions at {\pm\infty} and at zero the problem has at least two nontrivial smooth solutions.

scholarly journals Symmetric Solutions of a Nonlinear Elliptic Problem with Neumann Boundary Condition

2012 ◽  
Vol 03 (11) ◽  
pp. 1686-1688
Author(s):  
Ana Magnolia Marin Ramirez ◽  
Ruben Dario Ortiz Ortiz ◽  
Joel Arturo Rodriguez Ceballos
Keyword(s):  
Boundary Condition ◽  
Elliptic Problem ◽  
Neumann Boundary Condition ◽  
Neumann Boundary ◽  
Nonlinear Elliptic Problem ◽  
Nonlinear Elliptic

scholarly journals Global Bifurcation of Positive Solutions of Asymptotically Linear Elliptic Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Ruyun Ma ◽  
Yanqiong Lu ◽  
Ruipeng Chen
Keyword(s):  
Positive Solutions ◽  
Elliptic Problem ◽  
Global Bifurcation ◽  
Elliptic Problems ◽  
Nonlinear Elliptic Problem ◽  
Asymptotically Linear ◽  
Bifurcation Theorem ◽  
Nonlinear Elliptic

We are concerned with determining values ofλ, for which there exist positive solutions of the nonlinear elliptic problem-Δu=λa(x)f(u)  in  Ω,∂u/∂n+b(x)g(u)=0  on  ∂Ω.The proof of our main results is based upon unilateral global bifurcation theorem of López-Gómez.

Multiple existence of solutions for a singularly perturbed nonlinear elliptic problem on a Riemannian manifold

2012 ◽  
Vol 142 (1) ◽  
pp. 81-114
Author(s):  
Norimichi Hirano
Keyword(s):  
Riemannian Manifold ◽  
Positive Solutions ◽  
Elliptic Problem ◽  
Existence Of Solutions ◽  
Singularly Perturbed ◽  
Nonlinear Elliptic Problem ◽  
Nonlinear Elliptic ◽  
Existence Of Positive Solutions ◽  
Image Position

Let (M, g) be a compact smooth N-dimensional Riemannian manifold without boundary. We consider the multiple existence of positive solutions of the problemwhere Δg stands for the Laplacian in M and f ε C2(M).

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