scientific article

zbMath1293.35093MaRDI QIDQ3378054

Marco Squassina

Publication date: 29 March 2006

Full work available at URL: http://www.emis.de/journals/EJDE/Monographs/07/abstr.html

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zbMATH Keywords

Palais-Smale conditionmultiple solutionssingularly perturbed equationsrelative categorynonexistence resultslack of compactnessvariational identitiesquasi-linear elliptic equationsweak slopeCritical pointsnon-smooth functionalsdeformation theoremcalculus of variations, Euler equationsinvariant functionals, mountain pass theoremquasi-linear variational inequalitiesspiked solutions

Mathematics Subject Classification ID

Nonsmooth analysis (49J52) Boundary value problems for second-order elliptic equations (35J25) Variational inequalities (global problems) in infinite-dimensional spaces (58E35) Multiplicity of solutions of equilibrium problems in solid mechanics (74G35) Variational methods for second-order elliptic equations (35J20) Research exposition (monographs, survey articles) pertaining to partial differential equations (35-02)

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The Caccioppoli ultrafunctions ⋮ Existence of minimizers for a quasilinear elliptic system of gradient type ⋮ Global compactness for a class of quasi-linear elliptic problems ⋮ On topological and metric critical point theory ⋮ Boundary behavior for a singular quasi-linear elliptic equation ⋮ Existence of nontrivial solutions for quasilinear elliptic equations at critical growth ⋮ Existence result for a class of singular quasilinear elliptic equations with critical growth ⋮ Diffeomorphism-invariant properties for quasi-linear elliptic operators ⋮ On Palais' principle for non-smooth functionals ⋮ Mountain pass solutions for quasi-linear equations via a monotonicity trick ⋮ Existence and concentration of positive solutions for a logarithmic Schrödinger equation via penalization method ⋮ Existence and multiplicity results for a class of coupled quasilinear elliptic systems of gradient type ⋮ Generalized solutions of variational problems and applications ⋮ On Explosive Solutions for a Class of Quasi-linear Elliptic Equations ⋮ Existence and multiplicity of solutions to Dirichlet problem for semilinear subelliptic equation with a free perturbation

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