Abstract:
The paper deals with nonlinear problems for equations of Grushin type. We prove some nonexistence results via Pokhozhaev's identity. In the rest of the paper we prove some results on smoothness near the boundary of eigenfunctions by using an explicit formula for fundamental solutions and the Kelvin transform for the operator.
This publication is cited in the following 31 articles:
N. Q. Nga, N. M. Tri, D. A. Tuan, “Pólya–Szegö type inequality and imbedding theorems for weighted Sobolev spaces”, Anal.Math.Phys., 14:2 (2024)
D. T. Luyen, N. M. Tri, D. A. Tuan, “Nontrivial solutions of the Dirichlet problems for semilinear degenerate elliptic equations”, Math. Notes, 116:5 (2024), 1051–1063
Luyen D.T. Cuong Ph.V., “Multiple Solutions to Boundary Value Problems For Semilinear Strongly Degenerate Elliptic Differential Equations”, Rend. Circ. Mat. Palermo, 71:1 (2022), 495–513
Duong Trong Luyen, Ha Tien Ngoan, Phung Thi Kim Yen, “Existence and Non-Existence of Solutions For Semilinear Bi-Delta(Gamma)-Laplace Equation”, Bull. Malays. Math. Sci. Soc., 45:2 (2022), 819–838
Alfalqi S., “Non-Existence Results For Stable Solutions to Weighted Elliptic Systems Including Advection Terms”, Mathematics, 10:2 (2022), 252
Duong Trong Luyen, Le Thi Hong Hanh, “Infinitely many solutions for perturbed Λγ-Laplace equations”, Georgian Mathematical Journal, 29:6 (2022), 863
Duong Trong Luyen, Le Thi Hong Hanh, “Three nontrivial solutions of boundary value problems for semilinear $\Delta_{\gamma}-$Laplace equation”, bspm, 40 (2022), 1
Xiaohuan Wang, Jihui Zhang, “Optimal Regularity of a Degenerate Elliptic Equation”, J Nonlinear Math Phys, 30:1 (2022), 254
Duong Trong Luyen, “Infinitely Many Solutions For Semilinear Strongly Degenerate Elliptic Differential Equations With Lack of Symmetry”, Acta Appl. Math., 175:1 (2021), 3
Duong Trong Luyen, Ninh Tien Nam, “Infinitely Many Solutions For Fourth-Order Semilinear Delta(Gamma) - Laplace Equation in R-N”, J. Elliptic Parabol. Equat., 7:2 (2021), 977–988
Lamberti P.D., Luzzini P., Musolino P., “Shape Perturbation of Grushin Eigenvalues”, J. Geom. Anal., 31:11 (2021), 10679–10717
Hamdani M.K., “Multiple Solutions For Grushin Operator Without Odd Nonlinearity”, Asian-Eur. J. Math., 13:7 (2020), 2050131
Luyen D.T. Tri N.M., “Infinitely Many Solutions For a Class of Perturbed Degenerate Elliptic Equations Involving the Grushin Operator”, Complex Var. Elliptic Equ., 65:12 (2020), 2135–2150
Duong Trong Luyen, “Existence of Nontrivial Solution For Fourth-Order Semilinear Delta(Gamma)-Laplace Equation R-N”, Electron. J. Qual. Theory Differ., 2019, no. 78, 1–12
Loiudice A., “Asymptotic Estimates and Nonexistence Results For Critical Problems With Hardy Term Involving Grushin-Type Operators”, Ann. Mat. Pura Appl., 198:6 (2019), 1909–1930
Duong Trong Luyen Nguyen Mirth Tri, “Existence of Infinitely Many Solutions For Semilinear Degenerate Schrodinger Equations”, J. Math. Anal. Appl., 461:2 (2018), 1271–1286
Rahal B. Hamdani M.K., “Infinitely Many Solutions For Delta(Alpha)-Laplaceequations With Sign-Changing Potential”, J. Fixed Point Theory Appl., 20:4 (2018), UNSP 137
Kogoj A.E. Lanconelli E., “Linear and Semilinear Problems Involving Delta(Lambda)-Laplacians”, Electron. J. Differ. Equ., 2018, no. 25, 167–178
D. T. Luyen, “Two Nontrivial Solutions of Boundary-Value Problems for Semilinear $\Delta_{\gamma}$-Differential Equations”, Math. Notes, 101:5 (2017), 815–823
Mihailescu M., Stancu-Dumitru D., Varga C., “on the Spectrum of a Baouendi-Grushin Type Operator: An Orlicz-Sobolev Space Setting Approach”, NoDea-Nonlinear Differ. Equ. Appl., 22:5 (2015), 1067–1087