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Global boundedness for generalized Schrödinger-type double phase problems in $${{\mathbb {R}}}^N$$ R N and applications to supercritical double phase problems

Author

Listed:
  • Hoang Hai Ha

    (Ho Chi Minh City University of Technology (HCMUT), Department of Mathematics, Faculty of Applied Science
    Vietnam National University Ho Chi Minh City)

  • Ky Ho

    (University of Economics Ho Chi Minh City, Department of Mathematics and Statistics)

  • Bui The Quan

    (Ho Chi Minh City University of Education, Group of Analysis and Applied Mathematics, Department of Mathematics)

  • Inbo Sim

    (University of Ulsan, Department of Mathematics)

Abstract

We establish two global boundedness results for weak solutions to generalized Schrödinger-type double phase problems with variable exponents in $${{\mathbb {R}}}^N$$ R N under new critical growth conditions optimally introduced in Ha and Ho (J Math Anal Appl 541:128748, 2025) and Ho and Winkert (Calc Var Partial Differ Equ 62(8):227, 2023). More precisely, for the case of subcritical growth, we employ the De Giorgi iteration with a suitable localization method in $${{\mathbb {R}}}^N$$ R N to obtain a priori bounds. As a byproduct, we derive the decay property of weak solutions. For the case of critical growth, using the De Giorgi iteration with a localization adapted to the critical growth, we prove the global boundedness. As an interesting application of these results, the existence of weak solutions for supercritical double phase problems is shown. These results are new even for problems with constant exponents in $${{\mathbb {R}}}^N$$ R N .

Suggested Citation

  • Hoang Hai Ha & Ky Ho & Bui The Quan & Inbo Sim, 2026. "Global boundedness for generalized Schrödinger-type double phase problems in $${{\mathbb {R}}}^N$$ R N and applications to supercritical double phase problems," Partial Differential Equations and Applications, Springer, vol. 7(3), pages 1-33, June.
    • Handle: RePEc:spr:pardea:v:7:y:2026:i:3:d:10.1007_s42985-026-00389-8
    DOI: 10.1007/s42985-026-00389-8
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