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2006, 1st ed., Mathematics in science and engineering, ISBN 9780444522009, Volume 205, 502
This book introduces the method of lower and upper solutions for ordinary differential equations. This method is known to be both easy and powerful to solve... 
Boundary value problems | Functional differential equations
eBook
Journal of Differential Equations, ISSN 0022-0396, 05/2017, Volume 262, Issue 10, pp. 5231 - 5270
We consider the boundary value problem(Pλ)−Δu=λc(x)u+μ(x)|∇u|2+h(x),u∈H01(Ω)∩L∞(Ω), where Ω⊂RN,N≥3 is a bounded domain with smooth boundary. It is assumed that... 
Lower and upper solutions | Quasilinear elliptic equations | Quadratic growth in the gradient | MATHEMATICS | MAXIMUM PRINCIPLE | QUADRATIC GROWTH | EQUATIONS | UNIQUENESS | Analysis of PDEs | Mathematics
Journal Article
Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 6/2018, Volume 57, Issue 3, pp. 1 - 42
We consider the boundary value problem where $$\Omega \subset \mathbb {R}^{N}$$ Ω⊂RN , $$N \ge 2$$ N≥2 , is a bounded domain with smooth boundary. We assume... 
35J20 | Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | 35J92 | Mathematics | 35J25 | SOURCE TERMS | MATHEMATICS | MATHEMATICS, APPLIED | RABINOWITZ-TYPE CONDITION | REGULARITY | NATURAL GROWTH | EQUATIONS | NONLINEARITIES | PRINCIPLE
Journal Article
Nonlinear Analysis, ISSN 0362-546X, 04/2019, Volume 181, pp. 9 - 23
This paper deals with the quasilinear elliptic problem − div∇u∕1+|∇u|2+a(x)u=b(x)∕1+|∇u|2inB,u=0on∂B,where B is an open ball in RN, with N≥2, and a,b∈C1(B¯)... 
Classical solution | Prescribed mean curvature equation | Uniqueness | A priori bound | Comparison principle | Dirichlet boundary condition | Existence | CORNEAL | MATHEMATICS | MATHEMATICS, APPLIED | MODEL | MEAN-CURVATURE EQUATION | Anisotropy | Cornea | Computational fluid dynamics | Capillarity | Optometry | Dirichlet problem | Elliptic functions | Curvature | Compressible fluids
Journal Article
Journal of Functional Analysis, ISSN 0022-1236, 04/2015, Volume 268, Issue 8, pp. 2298 - 2335
We consider the boundary value problem(Pλ)u∈H01(Ω)∩L∞(Ω):−Δu=λc(x)u+μ(x)|∇u|2+h(x), where Ω⊂RN, N≥3 is a bounded domain with smooth boundary. It is assumed... 
Quadratic growth in the gradient | Topological degree | Continuum of solutions | Elliptic equations | EXISTENCE | MATHEMATICS | Topological | QUADRATIC GROWTH | EQUATIONS | UNIQUENESS | Analysis of PDEs | Mathematics
Journal Article
Positivity, ISSN 1385-1292, 12/2017, Volume 21, Issue 4, pp. 1319 - 1340
Journal Article
Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 9/2015, Volume 54, Issue 1, pp. 349 - 363
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 03/2016, Volume 260, Issue 5, pp. 4572 - 4618
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 12/2014, Volume 420, Issue 1, pp. 772 - 780
In this note we present some uniqueness and comparison results for a class of problem of the form(0.1)−Lu=H(x,u,∇u)+h(x),u∈H01(Ω)∩L∞(Ω), where Ω⊂RN, N≥2 is a... 
Uniqueness of solution | Quasilinear elliptic equations | Quadratic growth in the gradient | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
Mathematische Nachrichten, ISSN 0025-584X, 06/2015, Volume 288, Issue 8-9, pp. 854 - 871
The biharmonic Dirichlet boundary value problem on a bounded domain is the focus of the present paper. By Riesz' representation theorem the existence and... 
35J40 | 74K20 | Biharmonic operator | Corner domains | MATHEMATICS | SYSTEMS | EQUATION | STOKES
Journal Article
Positivity, ISSN 1385-1292, 12/2015, Volume 19, Issue 4, pp. 843 - 875
In this paper we are interested in the following fourth order eigenvalue problem coming from the buckling of thin films on liquid substrates: $$\begin{aligned}... 
Operator Theory | Fourier Analysis | Nodal properties of eigenfunctions | Potential Theory | Calculus of Variations and Optimal Control; Optimization | 35B65 | Mathematics | Fourth order problem | Econometrics | Buckling | 35K55 | MATHEMATICS | Thin films | Analysis | Dielectric films | Studies | Topological manifolds | Mathematical analysis | Asymptotic methods | Eigen values
Journal Article
Advanced Nonlinear Studies, ISSN 1536-1365, 2013, Volume 13, Issue 1, pp. 97 - 114
We consider the resonant-superlinear elliptic problem -Delta u = lambda(1)u + (u(+))(q) + f(x), with Dirichlet boundary conditions on a bounded regular domain... 
Lower and upper solutions | Semilinear elliptic problems | Resonance | Superlinear | MATHEMATICS | superlinear | MATHEMATICS, APPLIED | lower and upper solutions | resonance
Journal Article
Advances in Differential Equations, ISSN 1079-9389, 2011, Volume 16, Issue 3-4, pp. 221 - 256
Journal Article
Nonlinear Differential Equations and Applications NoDEA, ISSN 1021-9722, 12/2009, Volume 16, Issue 6, pp. 745 - 769
In the first part of this work, we recall variational methods related to invariant sets in $${C^1_0}$$ . In the second part of the work, we consider an... 
35J20 | 35B05 | Mathematics | 35J60 | Analysis | EXISTENCE | ORDER | MATHEMATICS, APPLIED | POSITIVE SOLUTIONS | SETS | BOUNDARY-VALUE-PROBLEMS | EQUATIONS | JUMPING NONLINEARITIES | CRITICAL-POINT
Journal Article
Differential and Integral Equations, ISSN 0893-4983, 05/2013, Volume 26, Issue 5-6, pp. 603 - 622
Journal Article
Advances in Differential Equations, ISSN 1079-9389, 2011, Volume 16, Issue 1-2, pp. 165 - 198
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 2008, Volume 244, Issue 3, pp. 599 - 629
In this paper we prove some existence results of semilinear Dirichlet problems in nonsmooth domains in presence of lower and upper solutions well-ordered or... 
Lower and upper solutions | Semilinear Dirichlet problem | Nonsmooth domains | MATHEMATICS | lower and upper solutions | BOUNDARY-VALUE PROBLEMS | EQUATIONS | nonsmooth domains | ORDERED LOWER | semilinear dirichlet problem
Journal Article
Bulletin of the Belgian Mathematical Society - Simon Stevin, ISSN 1370-1444, 12/2011, Volume 18, Issue 5, p. 769
We consider the heat equation on a polygonal domain [OMEGA] of the plane in weighted [L.sup.p]-Sobolev spaces 
Singularities (Mathematics) | Heat equation | Series, Dirichlet | Research | Vector spaces | Cauchy problem
Journal Article
Rendiconti dell'Istituto di Matematica dell'Universita di Trieste, ISSN 0049-4704, 2012, Volume 44, Issue 1, pp. 259 - 284
Journal Article
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