Pavol Quittner — Papers 
[73] 
Liouville theorems for scaling invariant superlinear
parabolic problems with gradient structure,
Preprint 2014
(PDF
210kB)

[72] 
A priori estimates, existence and Liouville theorems
for semilinear elliptic systems with power nonlinearities,
Nonlinear Analysis TM&A 102 (2014), 144158

[71]  (with Ph. Souplet)
Symmetry of components for semilinear elliptic systems,
SIAM J. Math. Anal. 44 (2012), 25452559

[70]  (with Ph. Souplet)
Optimal Liouvilletype theorems for noncooperative
elliptic Schrodinger systems and applications
,
Commun. Math. Phys. 311 (2012), 119

[69]  (with Ph. Souplet)
Blowup rate of solutions of parabolic poblems
with nonlinear boundary conditions
,
Discrete Contin. Dynam. Systems S 5 (2012), 671681

[68]  (with Ph. Souplet)
Parabolic Liouvilletype theorems via their elliptic counterparts
,
Discrete Contin. Dynam. Systems, Supplement 2011
(Proc. 8th AIMS Intern. Conf. on Dynamical Systems,
Differ. Equations and Applications, Dresden 2010), 12061213

[67]  (with I. Kosirova)
Boundedness, a priori estimates
and existence of solutions of elliptic systems
with nonlinear boundary conditions
,
Adv. Differ. Equations 16 (2011), 601622

[66]  (with T. Bartsch and P. Polacik)
Liouvilletype theorems and asymptotic behavior of nodal radial solutions
of semilinear heat equations,
J. European Math. Soc. 13 (2011), 219247

[65]  (with S. Kelemen)
Boundedness and a priori estimates
of solutions to elliptic systems
with DirichletNeumann boundary conditions,
Commun. Pure Appl. Anal. 9 (2010), 731740

[64]  (with W. Reichel)
Very weak solutions to elliptic equations with nonlinear Neumann
boundary conditions,
Calc. Var. 32 (2008), 429452

[63]  (with P. Polacik)
Asymptotic behavior of threshold and subthreshold solutions
of a semilinear heat equation,
Asymptotic Analysis 57 (2008), 125141

[62]  (with N. Ackermann, T. Bartsch and P. Kaplicky)
A priori bounds, nodal equlibria and connecting orbits
in indefinite superlinear parabolic problems,
Trans. Amer. Math. Soc. 360 (2008), 34933539

[61] 
The decay of global solutions of a semilinear heat equation,
Discrete Contin. Dynam. Systems A 21 (2008), 307318

[60] 
Qualitative theory of semilinear parabolic equations and systems,
In: Topics on Partial Differential Equations,
Lecture notes of the Jindrich Necas Center for Mathematical Modeling,
Vol. 2, eds. P. Kaplicky and S. Necasova,
Matfyzpress, Praha, 2007, pp. 159199

[59]  (with P. Polacik and Ph. Souplet)
Singularity and decay estimates in superlinear
problems via Liouvilletype theorems,
I: Elliptic equations and systems,
Duke Math. J. 139 (2007), 555579

[58]  (with P. Polacik and Ph. Souplet)
Singularity and decay estimates in superlinear
problems via Liouvilletype theorems.
Part II: Parabolic equations,
Indiana Univ. Math. J. 56 (2007), 879908

[57]  (with P. Polacik)
A Liouvilletype theorem and the decay of radial solutions of a semilinear heat equation,
Nonlinear Analysis TM&A 64 (2006), 16791689

[56]  (with H. Amann)
Optimal control problems governed by semilinear parabolic equations
with low regularity data,
Advances in Differ. Equations 11 (2006), 133

[55]  (with J. LopezGomez)
Complete and energy blowup in indefinite superlinear parabolic problems,
Discrete Contin. Dynam. Systems A 14 (2006), 169186

[54]  (with P. Polacik)
Liouville type theorems and complete blowup
for indefinite superlinear parabolic equations,
In Nonlinear Elliptic and Parabolic Problems, M. Chipot and J. Escher (eds.),
Progress in Nonlinear Differential Equations and Their Applications,
Vol. 64, Birkhauser, Basel, 2005, 391402

[53]  (with H. Amann)
Optimal control problems with final observation
governed by explosive parabolic equations,
SIAM J. Control Optimization 44 (2005), 12151238

[52]  (with A. RodriguezBernal)
Complete and energy blowup
in parabolic problems with nonlinear boundary conditions,
Nonlinear Analysis TM&A 62 (2005), 863875

[51]  (with F. Simondon)
A priori bounds and complete blowup of positive solutions
of indefinite superlinear parabolic problems,
J. Math. Anal. Appl. 304 (2005), 614631

[50] 
Complete and energy blowup in superlinear parabolic problems,
Recent Advances in Elliptic and Parabolic Problems:
Proceedings of the International Conference
Hsinchu, Taiwan 1620 February 2004,
eds. ChiunChuan Chen, Michel Chipot and ChangShou Lin,
World Scientific 2005, 217229

[49] 
Equilibria and connecting orbits in superlinear parabolic problems
via a priori bounds of global solutions,
Gakuto International Series,
Math. Sciences and Applications 20,
(Proc. of the intern. conf. "Nonlinear Partial Differential Equations
and Their Applications", Fudan Univ., Shanghai 2003,
N.Kenmochi, M.Otani, S.Zheng, eds.),
Gakkotosho, Tokyo, 2004, 526534

[48]  (with Ph. Souplet)
A priori estimates and existence for elliptic systems via bootstrap
in weighted Lebesgue spaces,
Archive Rational Mech. Anal. 174 (2004), 4981

[47]  (with M. Chipot)
Equilibria, connecting orbits and a priori bounds for semilinear
parabolic equations with nonlinear boundary conditions,
J. Dynamics Differ. Equations 16 (2004), 91138

[46] 
Multiple equilibria, periodic solutions and a priori bounds for solutions in superlinear parabolic problems,
NoDEA, 11 (2004), 237258

[45]  (with Ph. Souplet and M. Winkler)
Initial blowup rates and universal bounds for nonlinear heat equations,
J. Differ. Equations 196 (2004), 316339

[44]  (with H. Amann)
Semilinear parabolic equations involving measures and low regularity data,
Trans. Amer. Math. Soc. 356 (2004), 10451119

[43]  (with Ph. Souplet)
Bounds of global solutions of parabolic problems with nonlinear boundary conditions,
Indiana Univ. Math. J. 52 (2003), 875900

[42] 
Continuity of the blowup time and a priori bounds for solutions in superlinear parabolic problems,
Houston J. Math. 29 (2003), 757799

[41]  (with M. Chlebik and M. Fila)
Blowup of positive solutions of a semilinear parabolic equation with a gradient term,
Dyn. Contin. Discrete Impulsive Syst. 10 (2003), 525537

[40]  (with Ph. Souplet)
A priori estimates of global solutions of superlinear parabolic problems without variational structure,
Discrete Contin. Dyn. Systems A 9 (2003), 12771292

[39] 
Superlinear elliptic and parabolic problems,
Proc. Sem. Diff. Equations
(Pavlov, May 2731, 2002), Univ. of West Bohemia in Pilsen, 2003, 73167

[38] 
A priori bounds for solutions of parabolic problems and applications,
Proc. Equadiff 10, Math. Bohemica 127 (2002), 329341

[37]  (with Ph. Souplet)
Global existence from singlecomponent $L_p$ estimates in a semilinear reactiondiffusion system,
Proc. AMS 130 (2002), 27192724

[36]  (with Ph. Souplet)
Admissible $L_p$ norms for local existence and for continuation in
semilinear parabolic systems are not the same,
Proc. Roy. Soc. Edinburgh A 131 (2001), 14351456

[35]  (with J.M. Arrieta and A. RodriguezBernal)
Parabolic problems with nonlinear dynamical boundary conditions and singular initial data,
Differ. Integral Equations 14 (2001), 14871510

[34] 
Universal bound for global positive solutions of a superlinear parabolic problem,
Math. Ann. 320 (2001), 299305

[33] 
A priori estimates of solutions of superlinear problems,
Math. Bohemica 126 (2001), 483492

[32] 
A priori estimates for global solutions and multiple equilibria
of a superlinear parabolic problem involving measures,
Electron. J. Diff. Eqns. 2001(2001), No.29, 117

[31] 
Global existence for semilinear parabolic problems,
Adv. Math. Sci. Appl. 10 (2000), 643660

[30] 
A priori bounds for global solutions of a semilinear parabolic problem,
Acta Math. Univ. Comenianae 68 (1999), 195203
(PostScript 283kB,
gzip'd PostScript 138kB)

[29]  (with M. Fila)
The blowup rate for a semilinear parabolic system,
J. Math. Anal. Appl. 238 (1999), 468476

[28]  (with H. Amann)
Elliptic boundary value problems involving measures: existence, regularity,
and multiplicity,
Advances in Diff. Equations 3 (1998), 753813

[27] 
Signed solutions for a semilinear elliptic problem,
Diff. Integral Equations 11 (1998), 551559

[26]  (with M. Fila)
Large Time Behavior of Solutions of a Semilinear Parabolic Equation
with a Nonlinear Dynamical Boundary Condition,
Topics in Nonlinear Analysis. The Herbert Amann Anniversary Volume,
Birkhauser Verlag 1998, pp.251272
(Errata)

[25] 
Global solutions in parabolic blowup problems with perturbations,
Progress in partial differ. equations
(Proc. 3rd European Conf. on Elliptic and Parabolic Problems, PontaMousson 1997,
eds. H. Amann, C. Bandle, M. Chipot, F. Conrad and I. Shafrir),
Pitman Res. Notes in Math. Ser. 384, Vol. 2 (1998) 7791

[24] 
Transition from decay to blowup in a parabolic system,
Archivum mathematicum 34 (1998), 199206 (
PostScript 342kB,
gzip'd PostScript 145kB)

[23]  (with M. Fila)
Global solutions of the Laplace equation with
a nonlinear dynamical boundary condition,
Math. Meth. Appl. Sci. 20 (1997), 13251333

[22] 
Global existence of solutions of parabolic problems with nonlinear
boundary conditions,
Banach Center Publications 33 (1996), 309314

[21]  (with H. Amann)
A nodal theorem for coupled system of Schroedinger
equations and the number of bound states,
J. Math. Phys. 36 (1995), 45534560

[20] 
Boundedness of trajectories of parabolic equations and stationary solutions
via dynamical methods,
Diff. Integral Equations 7 (1994), 15471556

[19] 
On global existence and stationary solutions for two classes of semilinear
parabolic problems,
Comment. Math. Univ. Carolinae 34 (1993), 105124 (
PostScript 555kB,
gzip'd PostScript 136kB;
First page is shifted to the end)

[18] 
(with M. Fila) Radial positive solutions for a semilinear elliptic equation
with a gradient term,
Adv. Math. Sci. Appl. 2 (1993), 3945

[17] 
Blow up for semilinear parabolic equations with a gradient term,
Math. Meth. Appl. Sci. 14 (1991), 413417

[16]  (with M. Fila)
The blowup rate for the heat equation with a nonlinear
boundary condition,
Math. Meth. Appl. Sci. 14 (1991), 197205

[15]  (with M. Chipot and M. Fila)
Stationary solutions, blow up and convergence to stationary solutions
for semilinear parabolic equations with nonlinear boundary conditions,
Acta Math. Univ. Comenianae 60 (1991), 35103 (
PostScript 6663kB,
gzip'd PostScript 537kB)

[14]  (with M. Fila and J. Hulshof)
The quenching problem on the Ndimensional ball,
In Nonlinear Diffusion Problems and their Equilibrium States 3
(eds. N.G. Lloyd, W.M. Ni, L.A. Peletier, J. Serrin)
Birkhauser, BostonBaselBerlin 1992, 183196

[13] 
Stability of stationary solutions of parabolic variational inequalities,
In Differential Equations and their Applications
(Proc. of the Conference EQUADIFF 7, Praha 1989, ed. J. Kurzweil),
Teubner Texte zur Math. 118, Teubner, Leipzig 1990, 191194

[12] 
An instability criterion for variational inequalities,
Nonl. Analysis TM&A 15 (1990), 11671180

[11] 
A remark on the stability of stationary solutions of parabolic variational inequalities,
Czechoslovak Math. J. 40 (1990), 472474

[10] 
On positive solutions of semilinear elliptic problems,
Comment. Math. Univ. Carol. 30 (1989), 579585

[9] 
Solvability and multiplicity results for variational inequalities,
Comment. Math. Univ. Carol. 30 (1989), 281302

[8] 
On the principle of linearized stability for variational inequalities,
Math. Ann. 283 (1989), 257270

[7]  (with M. Mosko and I. Novak)
On the analytical approach to the RSET in GaAsAlGaAs heterostructures,
SolidState Electronics 31 (1988), 363366

[6] 
Bifurcation points and eigenvalues of inequalities of reactiondiffusion type,
J. reine angew. Math. 380 (1987), 113

[5] 
Spectral analysis of variational inequalities,
Comment. Math. Univ. Carol. 27 (1986), 605629

[4]  (with D. Zubrinic)
On the unique slovability of nonresonant elliptic equations,
Comment. Math. Univ. Carol. 27 (1986), 301306

[3] 
A note to E. Miersemann's papers on higher eigenvalues of variational inequalities,
Comment. Math. Univ. Carol. 26 (1985), 665674

[2] 
Singular sets and number of solutions of nonlinear boundary value problems,
Comment. Math. Univ. Carol. 24 (1983), 371385

[1] 
Generic properties of von Karman equations,
Comment. Math. Univ. Carol. 23 (1982), 399413
