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Mathematics
Irina Meghea
Summary: This study presents a new result concerning the existence of solutions for mathematical physics problems involving p-Laplacian and p-pseudo-Laplacian, based on a variant of the Mountain Pass Theorem (MPT). The novelty of the research lies in formulating the central result under weaker conditions, proving this statement, and applying it to solve problems such as nonlinear elastic membrane, glacier sliding, and pseudo torsion. Additionally, the study suggests specific numerical methods for constructing the appropriate solutions.
Article
Mathematics, Applied
Yane Araujo, Eudes Barboza, Gilson de Carvalho
Summary: This paper studies the existence of solutions for integrodifferential Schrödinger equations with specific structural properties, which include a nonlocal operator, a bounded potential, and a nonlinear term with critical exponential growth.
APPLICABLE ANALYSIS
(2023)
Article
Mathematics, Applied
Xiaoping Wang, Fangfang Liao, Fulai Chen
Summary: In this paper, the planar Schrodinger-Poisson system is considered and converted to an integro-differential equation with logarithmic convolution potential. The existence of an axially symmetric mountain-pass type solution is proven using new estimates on logarithmic convolution potential. These results improve upon previous research by Chen and Tang (2020) and others.
APPLIED MATHEMATICS LETTERS
(2024)
Article
Mathematics, Applied
Yony Raul Santaria Leuyacc
Summary: This paper deals with the existence of nontrivial solutions to a class of strongly coupled Hamiltonian systems. The approach combines Trudinger-Moser type inequalities for weighted Sobolev spaces and variational methods.
Article
Mathematics, Applied
Reshmi Biswas, Sarika Goyal, Konijeti Sreenadh
Summary: In this paper, we investigate the existence of positive solutions for a class of quasilinear Choquard equations involving N-Laplacian and nonlinearity with critical exponential growth.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Computer Science, Interdisciplinary Applications
Michaela Bailova, Jiri Bouchala
Summary: This paper deals with a specific type of boundary value problem with Dirichlet boundary conditions and p-Laplacian, showing two ways to prove the existence of nontrivial weak solutions and introducing a new minimax theorem. A numerical algorithm based on this method is presented, demonstrating its efficiency through numerical examples and comparison with a current approach.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2021)
Article
Mathematics, Applied
Shengbing Deng, Tingxi Hu, Chun-Lei Tang
Summary: This paper proves the existence of a nontrivial solution for a specific boundary value problem within the unit ball, meeting certain criteria.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
(2021)
Article
Mathematics, Applied
Suellen Cristina Q. Arruda, Rubia G. Nascimento
Summary: This paper demonstrates the existence and multiplicity of positive solutions using the sub-supersolution method and Mountain Pass Theorem in a general singular system, where the operator is neither homogeneous nor linear.
ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS
(2021)
Article
Mathematics
Xiaoyan Lin, X. H. Tang
Summary: In this paper, we consider the existence of a mountain-pass type solution for the nonlinear Chern-Simons-Schrodinger equations. By combining various methods, including variational methods and Trudinger-Moser inequality, we prove the existence of such a solution under certain weak assumptions.
COMPLEX VARIABLES AND ELLIPTIC EQUATIONS
(2023)
Article
Mathematics, Applied
Anna Maria Candela, Kanishka Perera, Caterina Sportelli
Summary: In this paper, we derive a new existence result for a class of N-Laplacian problems where the classical N-Laplacian is replaced by an operator with coefficients depending on the solution. We allow a supercritical growth for the nonlinear term, despite the difficulty introduced by the coefficients. Our proof relies on the interaction between two different norms, a weak version of the Cerami-Palais-Smale condition, and a proper decomposition of the ambient space. By applying a suitable generalization of the Ambrosetti-Rabinowitz Mountain Pass Theorem, we establish the existence of at least one nontrivial bounded solution. (c) 2022 Elsevier Ltd. All rights reserved.
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
(2023)
Article
Mathematics, Applied
Shuai Yuan, Xianhua Tang, Sitong Chen
Summary: In this paper, we study the existence of nontrivial solutions for a one-dimensional fractional Schrodinger equation with exponential critical growth. Compared to existing works, our analysis faces new challenges due to weaker assumptions on the reaction term. By employing sharp energy estimates, we provide a detailed analysis of the energy level and establish the existence of nontrivial solutions for a wider class of nonlinear terms. Additionally, we use the non-Nehari manifold method to establish the existence of Nehari-type ground state solutions for the one-dimensional fractional Schrodinger equation.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics
Ning Zhang, Xianhua Tang, Sitong Chen
Summary: In this paper, we investigate a non-linear Chern-Simons-Schrodinger equation and establish a new version of Trudinger-Moser inequality in the associated energy functional's working space. By combining variational methods and estimating the minimax level of the energy functional, we prove the existence of a solution for the equation under some weak assumptions.
JOURNAL OF GEOMETRIC ANALYSIS
(2023)
Article
Mathematics
Mengfei Tao, Binlin Zhang
Summary: In this paper, we study the existence of nontrivial weak solutions for fractional p-Laplacian equations with exponential growth and Hardy term. We use a fixed point result and singular Trudinger-Moser inequality in R-N to obtain the desired results.
COMPLEX VARIABLES AND ELLIPTIC EQUATIONS
(2023)
Article
Mathematics, Applied
Zhang Binlin, Xiumei Han, Nguyen Van Thin
Summary: In this paper, we investigate the existence of a solution to Schrodinger-Kirchhoff-type problems with a nonlocal integro-differential operator and the Trudinger-Moser nonlinearity. By applying the mountain pass theorem, we establish the existence of solutions in appropriate Sobolev spaces. An important feature of our study is the consideration of degenerate cases where the Kirchhoff function is zero.
APPLICABLE ANALYSIS
(2023)
Article
Mathematics, Applied
Manasses de Souza, Uberlandio B. Severo, Thiago Luiz O. do Rego
Summary: This work investigates the existence and multiplicity of solutions for a class of nonlocal problems involving the fractional N/s-Laplacian and nonlinearities with exponential growth. The existence of a least energy nodal solution is established using constraint variational method and fractional Trudinger-Moser inequality, while minimax techniques are exploited to prove the existence of nonnegative and nonpositive ground state solutions. The energy of the nodal solution is shown to be strictly larger than twice the ground state energy.
NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS
(2021)
