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), 144-158
[71](with Ph. Souplet) Symmetry of components for semilinear elliptic systems, SIAM J. Math. Anal. 44 (2012), 2545-2559
[70](with Ph. Souplet) Optimal Liouville-type theorems for noncooperative elliptic Schrodinger systems and applications , Commun. Math. Phys. 311 (2012), 1-19
[69](with Ph. Souplet) Blow-up rate of solutions of parabolic poblems with nonlinear boundary conditions , Discrete Contin. Dynam. Systems S 5 (2012), 671-681
[68](with Ph. Souplet) Parabolic Liouville-type 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), 1206-1213
[67](with I. Kosirova) Boundedness, a priori estimates and existence of solutions of elliptic systems with nonlinear boundary conditions , Adv. Differ. Equations 16 (2011), 601-622
[66](with T. Bartsch and P. Polacik) Liouville-type theorems and asymptotic behavior of nodal radial solutions of semilinear heat equations, J. European Math. Soc. 13 (2011), 219-247
[65](with S. Kelemen) Boundedness and a priori estimates of solutions to elliptic systems with Dirichlet-Neumann boundary conditions, Commun. Pure Appl. Anal. 9 (2010), 731-740
[64](with W. Reichel) Very weak solutions to elliptic equations with nonlinear Neumann boundary conditions, Calc. Var. 32 (2008), 429-452
[63](with P. Polacik) Asymptotic behavior of threshold and sub-threshold solutions of a semilinear heat equation, Asymptotic Analysis 57 (2008), 125-141
[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), 3493-3539
[61] The decay of global solutions of a semilinear heat equation, Discrete Contin. Dynam. Systems A 21 (2008), 307-318
[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. 159-199
[59](with P. Polacik and Ph. Souplet) Singularity and decay estimates in superlinear problems via Liouville-type theorems, I: Elliptic equations and systems, Duke Math. J. 139 (2007), 555-579
[58](with P. Polacik and Ph. Souplet) Singularity and decay estimates in superlinear problems via Liouville-type theorems. Part II: Parabolic equations, Indiana Univ. Math. J. 56 (2007), 879-908
[57](with P. Polacik) A Liouville-type theorem and the decay of radial solutions of a semilinear heat equation, Nonlinear Analysis TM&A 64 (2006), 1679-1689
[56](with H. Amann) Optimal control problems governed by semilinear parabolic equations with low regularity data, Advances in Differ. Equations 11 (2006), 1-33
[55](with J. Lopez-Gomez) Complete and energy blow-up in indefinite superlinear parabolic problems, Discrete Contin. Dynam. Systems A 14 (2006), 169-186
[54](with P. Polacik) Liouville type theorems and complete blow-up 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, 391-402
[53](with H. Amann) Optimal control problems with final observation governed by explosive parabolic equations, SIAM J. Control Optimization 44 (2005), 1215-1238
[52](with A. Rodriguez-Bernal) Complete and energy blow-up in parabolic problems with nonlinear boundary conditions, Nonlinear Analysis TM&A 62 (2005), 863-875
[51](with F. Simondon) A priori bounds and complete blow-up of positive solutions of indefinite superlinear parabolic problems, J. Math. Anal. Appl. 304 (2005), 614-631
[50] Complete and energy blow-up in superlinear parabolic problems, Recent Advances in Elliptic and Parabolic Problems: Proceedings of the International Conference Hsinchu, Taiwan 16-20 February 2004, eds. Chiun-Chuan Chen, Michel Chipot and Chang-Shou Lin, World Scientific 2005, 217-229
[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, 526-534
[48](with Ph. Souplet) A priori estimates and existence for elliptic systems via bootstrap in weighted Lebesgue spaces, Archive Rational Mech. Anal. 174 (2004), 49-81
[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), 91-138
[46] Multiple equilibria, periodic solutions and a priori bounds for solutions in superlinear parabolic problems, NoDEA, 11 (2004), 237-258
[45](with Ph. Souplet and M. Winkler) Initial blow-up rates and universal bounds for nonlinear heat equations, J. Differ. Equations 196 (2004), 316-339
[44](with H. Amann) Semilinear parabolic equations involving measures and low regularity data, Trans. Amer. Math. Soc. 356 (2004), 1045-1119
[43](with Ph. Souplet) Bounds of global solutions of parabolic problems with nonlinear boundary conditions, Indiana Univ. Math. J. 52 (2003), 875-900
[42] Continuity of the blow-up time and a priori bounds for solutions in superlinear parabolic problems, Houston J. Math. 29 (2003), 757-799
[41](with M. Chlebik and M. Fila) Blow-up of positive solutions of a semilinear parabolic equation with a gradient term, Dyn. Contin. Discrete Impulsive Syst. 10 (2003), 525-537
[40](with Ph. Souplet) A priori estimates of global solutions of superlinear parabolic problems without variational structure, Discrete Contin. Dyn. Systems A 9 (2003), 1277-1292
[39] Superlinear elliptic and parabolic problems, Proc. Sem. Diff. Equations (Pavlov, May 27-31, 2002), Univ. of West Bohemia in Pilsen, 2003, 73-167
[38] A priori bounds for solutions of parabolic problems and applications, Proc. Equadiff 10, Math. Bohemica 127 (2002), 329-341
[37](with Ph. Souplet) Global existence from single-component $L_p$ estimates in a semilinear reaction-diffusion system, Proc. AMS 130 (2002), 2719-2724
[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), 1435-1456
[35](with J.M. Arrieta and A. Rodriguez-Bernal) Parabolic problems with nonlinear dynamical boundary conditions and singular initial data, Differ. Integral Equations 14 (2001), 1487-1510
[34] Universal bound for global positive solutions of a superlinear parabolic problem, Math. Ann. 320 (2001), 299-305
[33] A priori estimates of solutions of superlinear problems, Math. Bohemica 126 (2001), 483-492
[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, 1-17
[31] Global existence for semilinear parabolic problems, Adv. Math. Sci. Appl. 10 (2000), 643-660
[30] A priori bounds for global solutions of a semilinear parabolic problem, Acta Math. Univ. Comenianae 68 (1999), 195-203 (PostScript 283kB, gzip'd PostScript 138kB)
[29](with M. Fila) The blow-up rate for a semilinear parabolic system, J. Math. Anal. Appl. 238 (1999), 468-476
[28](with H. Amann) Elliptic boundary value problems involving measures: existence, regularity, and multiplicity, Advances in Diff. Equations 3 (1998), 753-813
[27] Signed solutions for a semilinear elliptic problem, Diff. Integral Equations 11 (1998), 551-559
[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.251-272 (Errata)
[25] Global solutions in parabolic blow-up problems with perturbations, Progress in partial differ. equations (Proc. 3rd European Conf. on Elliptic and Parabolic Problems, Pont-a-Mousson 1997, eds. H. Amann, C. Bandle, M. Chipot, F. Conrad and I. Shafrir), Pitman Res. Notes in Math. Ser. 384, Vol. 2 (1998) 77-91
[24] Transition from decay to blow-up in a parabolic system, Archivum mathematicum 34 (1998), 199-206 ( 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), 1325-1333
[22] Global existence of solutions of parabolic problems with nonlinear boundary conditions, Banach Center Publications 33 (1996), 309-314
[21](with H. Amann) A nodal theorem for coupled system of Schroedinger equations and the number of bound states, J. Math. Phys. 36 (1995), 4553-4560
[20] Boundedness of trajectories of parabolic equations and stationary solutions via dynamical methods, Diff. Integral Equations 7 (1994), 1547-1556
[19] On global existence and stationary solutions for two classes of semilinear parabolic problems, Comment. Math. Univ. Carolinae 34 (1993), 105-124 ( 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), 39-45
[17] Blow up for semilinear parabolic equations with a gradient term, Math. Meth. Appl. Sci. 14 (1991), 413-417
[16](with M. Fila) The blow--up rate for the heat equation with a nonlinear boundary condition, Math. Meth. Appl. Sci. 14 (1991), 197-205
[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), 35-103 ( PostScript 6663kB, gzip'd PostScript 537kB)
[14](with M. Fila and J. Hulshof) The quenching problem on the N-dimensional ball, In Nonlinear Diffusion Problems and their Equilibrium States 3 (eds. N.G. Lloyd, W.M. Ni, L.A. Peletier, J. Serrin) Birkhauser, Boston-Basel-Berlin 1992, 183-196
[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, 191-194
[12] An instability criterion for variational inequalities, Nonl. Analysis TM&A 15 (1990), 1167-1180
[11] A remark on the stability of stationary solutions of parabolic variational inequalities, Czechoslovak Math. J. 40 (1990), 472-474
[10] On positive solutions of semilinear elliptic problems, Comment. Math. Univ. Carol. 30 (1989), 579-585
[9] Solvability and multiplicity results for variational inequalities, Comment. Math. Univ. Carol. 30 (1989), 281-302
[8] On the principle of linearized stability for variational inequalities, Math. Ann. 283 (1989), 257-270
[7](with M. Mosko and I. Novak) On the analytical approach to the RSET in GaAs-AlGaAs heterostructures, Solid--State Electronics 31 (1988), 363-366
[6] Bifurcation points and eigenvalues of inequalities of reaction-diffusion type, J. reine angew. Math. 380 (1987), 1-13
[5] Spectral analysis of variational inequalities, Comment. Math. Univ. Carol. 27 (1986), 605-629
[4](with D. Zubrinic) On the unique slovability of nonresonant elliptic equations, Comment. Math. Univ. Carol. 27 (1986), 301-306
[3] A note to E. Miersemann's papers on higher eigenvalues of variational inequalities, Comment. Math. Univ. Carol. 26 (1985), 665-674
[2] Singular sets and number of solutions of nonlinear boundary value problems, Comment. Math. Univ. Carol. 24 (1983), 371-385
[1] Generic properties of von Karman equations, Comment. Math. Univ. Carol. 23 (1982), 399-413