Higher order nonlinear elliptic equations

Monotone operators and generalizations (47H05) Nonlinear boundary value problems for linear elliptic equations (35J65) Boundary value problems for higher-order elliptic equations (35J40) Research exposition (monographs, survey articles) pertaining to partial differential equations (35-02)

Related Items

Hölder continuity of bounded generalized solutions for some degenerated quasilinear elliptic equations with natural growth terms, Probabilistic weak solutions for nonlinear stochastic evolution problems involving pseudomonotone operators

Cites Work

Dirichlet's problem for linear elliptic partial differential equations
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Saddle points and multiple solutions of differential equations
Spectral analysis of nonlinear operators
Sulle singolarità eliminabili delle soluzioni deboli di equazioni ellittiche quasi lineari di ordine 2m
Eigenvectors of nonlinear potential operators
Singularités éliminables pour des équations semi-linéaires
Hölder continuity of the solutions of some nonlinear elliptic systems
Behavior of solutions of the Dirichlet problem for quasilinear divergent higher-order elliptic equations in unbounded domains
Monotone (nonlinear) operators in Hilbert space
A Landesman-Lazer alternative theorem for a class of optimization problems
Non-homogeneous media and vibration theory
The Lyusternik-Schnirelman theory
Regularity of weak solutions to elliptic equations of arbitrary order
On Galerkin's method in the existence theory of quasilinear elliptic equations
Differentiability of the solutions of nonlinear elliptic systems with natural growth
Fredholm alternatives for nonlinear A-proper mappings with applications to nonlinear elliptic boundary value problems
Krasnoselskiĭ's main bifurcation theorem
A note on topological degree for potential operators
A nonlinear elliptic boundary value problem at resonance
A general approach to Morse theory
Some results on regularity for solutions of non-linear elliptic systems and quasi-regular functions
Rotation of potential vector fields
Bifurcation and asymptotic bifurcation for equations involving A-proper mappings with applications to differential equations
Existence and multiplicity results for nonlinear elliptic problems with linear part at resonance. The case of the simple eigenvalue
Morse theory and a non-linear generalization of the Dirichlet problem
Infinite dimensional manifolds and nonlinear elliptic eigenvalue problems
Lusternik-Schnirelman theory on Banach manifolds
Existence and regularity almost everywhere of solutions to elliptic variational problems among surfaces of varying topological type and singularity structure
Sulla regolarità delle soluzioni deboli di una classe di sistemi ellittici quasi-lineari
Équations et inéquations non linéaires dans les espaces vectoriels en dualité
Approximation methods and the generalized topological degree for nonlinear mappings in Banach spaces
Nonlinear elliptic boundary-value problems in Orlicz-Sobolev spaces
A sharp sufficient condition for solution of a nonlinear elliptic boundary value problem
Local bounds for solutions of higher order nonlinear elliptic partial differential equations
Orlicz-Sobolev spaces and imbedding theorems
Antipodes theorem for A-proper mappings and its applications to mappings of the modified type (S) or (S)+ and to mapping with the pm property
On nonlinear mappings of monotone type with respect to two Banach spaces
Topics in stability and bifurcation theory
The L\(^p\)-integrability of the partial derivatives of a quasiconformal mapping
Morse theory on Hilbert manifolds
Interior estimates for elliptic systems of partial differential equations
Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I
The degree of mapping, and its generalizations
Fixed point theory and nonlinear problems
Resonance, distributions and semilinear elliptic partial differential equations
A new proof of de Giorgi's theorem concerning the regularity problem for elliptic differential equations
Variational and topological methods in nonlinear problems
Solvability of Linear and Quasilinear Elliptic Boundary Value Problems via the A-Proper Mapping Theory
Nonresonance and existence for nonlinear elliptic boundary value problems
The method of contractor directions for nonlinear elliptic equations
On the approximation-solvability of equations involving 𝐴-proper and pseudo-𝐴-proper mappings
Über die Regularität der Lösungen quasilinearer elliptischer Differentialgleichungen höherer Ordnung am Rande des Gebietes
NON-LINEAR FREDHOLM MAPS AND THE LERAY-SCHAUDER THEORY
Existence and regularity of weak solutions to the Dirichletproblem for semilinear elliptic systems of higher order.
Nonlinear elliptic boundary value problems
On the smoothness of weak solutions of quasilinear equations in several variables and of variational problems
Quelques résultats de Višik sur les problèmes elliptiques non linéaires par les méthodes de Minty-Browder
Nonlinear eigenvalue problems and Galerkin approximations
Über Lösungsverzweigungen bei Potentialoperatoren
Nonlinear elliptic boundary value problems and the generalized topological degree
LJUSTERNIK‐SCHNIRELMANN Theorem and Nonlinear Eigenvalue Problems