**Contemporary Mathematics**

Volume: 595;
2013;
340 pp;
Softcover

MSC: Primary 35;
Secondary 34; 47; 58

Print ISBN: 978-0-8218-9861-1

Product Code: CONM/595

List Price: $111.00

Individual Member Price: $88.80

**Electronic ISBN: 978-1-4704-0993-7
Product Code: CONM/595.E**

List Price: $111.00

Individual Member Price: $88.80

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# Recent Trends in Nonlinear Partial Differential Equations II: Stationary Problems

Share this page *Edited by *
*James B. Serrin; Enzo L. Mitidieri; Vicenţiu D. Rădulescu*

This book is the second of two volumes that
contain the proceedings of the Workshop on Nonlinear Partial
Differential Equations, held from May 28–June 1, 2012, at the
University of Perugia in honor of Patrizia Pucci's 60th birthday.

The workshop brought together leading experts and researchers in
nonlinear partial differential equations to promote research and to
stimulate interactions among the participants. The workshop program
testified to the wide ranging influence of Patrizia Pucci on the field
of nonlinear analysis and partial differential equations.

In her own work, Patrizia Pucci has been a seminal influence in
many important areas: the maximum principle, qualitative analysis of
solutions to many classes of nonlinear PDEs (Kirchhoff problems,
polyharmonic systems), mountain pass theorem in the critical case,
critical exponents, variational identities, as well as various
degenerate or singular phenomena in mathematical physics. This same
breadth is reflected in the mathematical papers included in this
volume.

The companion volume (Contemporary Mathematics, Volume 594) is
devoted to evolution problems in nonlinear partial differential
equations.

#### Table of Contents

# Table of Contents

## Recent Trends in Nonlinear Partial Differential Equations II: Stationary Problems

- Thanks vii8 free
- Preface ix10 free
- On degree theory for quasilinear elliptic equations with natural growth conditions 112 free
- 1. Introduction 112
- 2. Topological degree in reflexive Banach spaces 213
- 3. Quasilinear elliptic equations with controllable growth conditions 314
- 4. Quasilinear elliptic equations with natural growth conditions 1021
- 5. Topological degree for quasilinear elliptic equations with natural growth conditions 1526
- References 1930

- Radial solutions for a Gelfand type quasilinear elliptic problem with quadratic gradient terms 2132
- Remarks on some quasilinear equations with gradient terms and measure data 3142
- The effect of a linear term in some nonlinear elliptic equations with singular data 5566
- Quantitative bounds for subcritical semilinear elliptic equations 6374
- 1. Introduction 6374
- 2. Maximum and comparison principles on small sets 6475
- 3. Global estimates I 6879
- 4. Reminder on quantitative local bounds 7283
- 5. Global estimates II. Boundary estimates and global Harnack inequalities 7384
- 6. Comparing solutions for different values of 𝑝 and the limit as 𝑝→1 8293
- 7. Appendix 8596
- Acknowledgment 8798
- References 8798

- Sub and supersolutions, invariant cones and multiplicity results for 𝑝-Laplace equations 91102
- 1. Introduction 91102
- 2. Statement of the main results 93104
- 3. Preliminaries 96107
- 4. Minimal energy solution between ordered sub-supersolutions 98109
- 5. Mountain pass solution in presence of multiple sub-supersolutions 101112
- 6. Existence of 𝐾-invariant open sets 104115
- 7. A four solutions theorem 109120
- 8. Additional 𝐾-invariance results 113124
- Acknowledgment 117128
- References 117128

- A Moser type inequality in Zygmund spaces without boundary conditions 121132
- Existence results for some systems of coupled fractional nonlinear Schrödinger equations 135146
- Ground states for pseudo-relativistic equations with combined power and Hartree-type nonlinearities 151162
- Local boundedness of solutions to some anisotropic elliptic systems 169180
- A symmetry result for semilinear cooperative elliptic systems 187198
- An application of Kato’s inequality to quasilinear elliptic problems 205216
- 1. Introduction 205216
- 2. Notations and definitions 206217
- 3. The general problem and main ideas 209220
- 4. The semilinear case 210221
- 5. The quasilinear case: S-𝑝-C operators 211222
- 6. The quasilinear case: W-𝑝-C operators 212223
- 7. W-1-C case 214225
- Acknowledgment 217228
- References 217228
- References 217228

- Multiplicity results for constrained Neumann problems 219230
- On the classification of entire local minimizers of the Ginzburg-Landau equation 231242
- A Liouville result on a half space 237248
- Singular elliptic systems of Lane-Emden type 253264
- Uniform estimates for polyharmonic Green functions in domains with small holes 263274
- Variational problems on the Sphere 273284
- Semilinear Neumann problems with indefinite and unbounded potential and crossing nonlinearity 293304
- Infinitely many solutions for fractional Laplace equations with subcritical nonlinearity 317328

#### Readership

Graduate students and research mathematicians interested in nonlinear partial differential equations.