Article
Mathematics, Applied
Ahmed Aberqi, Jaouad Bennouna, Omar Benslimane, Maria Alessandra Ragusa
Summary: This paper deals with the existence of at least two nonnegative nontrivial solutions to a pozTHORN-Laplacian system involving critical nonlinearity in the context of Sobolev spaces with variable exponents on complete manifolds. The main results are established by exploring Nehari's method and conducting a refined analysis on the associated fiber map and some variational techniques.
JOURNAL OF FUNCTION SPACES
(2022)
Article
Mathematics, Applied
Zhouji Ma, Xiaojun Chang
Summary: This paper investigates the nonlinear biharmonic Schrödinger equation with combined power-type nonlinearities in R-N space. By analyzing the behavior of the ground state energy with respect to the prescribed mass, the existence of normalized ground state solutions is established. Furthermore, it is proven that all ground states are local minima of the associated energy functional.
APPLIED MATHEMATICS LETTERS
(2023)
Article
Mathematics, Applied
Zexin Zhang, Zhitao Zhang
Summary: In this paper, the existence and properties of solutions to the p-Laplacian equation with a L-p-norm constraint are studied. The existence of positive radial ground states and infinitely many radial and nonradial solutions are proved using methods such as Schwarz rearrangement, Ekeland variational principle, minimax theorems, and fountain theorem type argument.
Article
Mathematics, Applied
Mohammed El Mokhtar ould El Mokhtar
Summary: In this paper, we investigate p-Laplace equations with singular nonlinearities and critical Sobolev exponent, and prove the existence of at least four distinct nontrivial solutions using the Nehari manifold, Mountain Pass theorem, and Maximum principle theorem.
JOURNAL OF FUNCTION SPACES
(2022)
Article
Physics, Multidisciplinary
Igor R. Klebanov
Summary: In this paper, a cubic field theory involving scalar and anticommuting scalar fields is formulated. The results are generalized to a class of symmetric field theories with specific critical dimensions. The critical theories are proposed to be the UV completions of sigma models with specific properties. The quintic field theory with OSp(1 vertical bar 4)) symmetry is of particular interest and is used to predict the critical behavior of a lattice system.
PHYSICAL REVIEW LETTERS
(2022)
Article
Mathematics, Applied
Makram Hamouda, Mohamed Ali Hamza
Summary: In this article, the blow-up of the damped wave equation in the scale-invariant case and in the presence of two nonlinearities is studied. The research shows that the behavior of the wave equation in the presence of the damping term mu/1+t u(t) is similar to the case without damping.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Mathematics, Applied
Patrizia Pucci, Letizia Temperini
Summary: This paper investigates the existence of entire nontrivial solutions for fractional (p, q) systems with critical Hardy terms in R-N, deriving solutions for the system via the mountain pass lemma. The study also introduces a simplified version of the main system and examines the behavior of PS sequences, improving previous results for fractional problems.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2021)
Article
Mathematics, Applied
Xiaojing Feng, Haidong Liu, Zhitao Zhang
Summary: In this paper, the existence and multiplicity of solutions to the Kirchhoff equation with Sobolev critical exponent under normalized constraint are studied. The cases of mu>0 and mu<=0 are distinguished, and the existence and nonexistence of solutions are proved under suitable assumptions. The asymptotic behavior of solutions as mu -> 0(+) and b -> 0(+) is investigated.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
(2023)
Article
Mathematics, Applied
Mengfei Tao, Binlin Zhang
Summary: This article investigates a class of nonhomogeneous fractional (p, q)-Laplacian systems with critical nonlinearities and critical Hardy nonlinearities in R-N. By utilizing a fixed point result and fractional Hardy-Sobolev inequality, the existence of nontrivial nonnegative solutions is established, with a consideration of Choquard-type nonlinearities as well. Furthermore, the corresponding existence results for the fractional (p, q)-Laplacian systems in the case of N = sp = lq are derived, highlighting the novelty of using fixed point argument in seeking solutions.
ADVANCES IN NONLINEAR ANALYSIS
(2022)
Article
Mathematics, Applied
Khaled Zennir, Abderrahmane Beniani, Belhadji Bochra, Loay Alkhalifa
Summary: This paper considers the initial value problem for the nonlinear dissipative wave equation containing the p(x)-bi-Laplacian operator. Sufficient conditions for the blow-up with nonpositive initial energy of a generalized solution are obtained in finite time using a wide variety of techniques.
Article
Mathematics, Applied
Jiayu Wang, Wei Han
Summary: This article discusses the existence and multiplicity of weak solutions for a p-q-Laplacian system with singular and critical nonlinearity within a suitable range of lambda.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Mathematics, Applied
Alessio Fiscella, Patrizia Pucci
Summary: This paper discusses the existence of nontrivial solutions for (p, N) equations in R-N with critical exponential growth, introducing a tricky step analysis and using a new lemma for exponential nonlinearities to obtain a multiplicity result.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2021)
Article
Mathematics
Jianghao Hao, Yajing Zhang
Summary: In this paper, we investigate the critical fractional equation with a parameter lambda and establish uniform lower bounds for ?, which is the supremum of the set of lambda values related to the existence of positive solutions of the critical fractional equation.
ACTA MATHEMATICA SCIENTIA
(2022)
Article
Mathematics, Applied
Mingzheng Sun, Jiabao Su, Binlin Zhang
Summary: In this paper, the Kirchhoff type equation with an additional critical nonlinear term is studied using Morse theory. The main results include computation of critical groups, including cases where zero is a mountain pass solution and the nonlinearity is resonant at zero. The estimates of the critical groups are found to be new even for Kirchhoff type equations with subcritical nonlinearities.
COMMUNICATIONS IN CONTEMPORARY MATHEMATICS
(2021)
Article
Mathematics, Applied
Heqian Lu, Zhengce Zhang
Summary: This article studies the Cauchy problem for the evolution p-Laplacian equation and investigates the local existence, global existence, and nonexistence of solutions. Specifically, an optimal Fujita-type result is obtained for the case where lambda > 0 and mu > 0, demonstrating the discontinuity phenomenon of the critical exponent caused by the positive gradient term. The existence and nonexistence of global solutions are also discussed for the case where lambda > 0 and mu < 0.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2022)
