This paper is devoted to demonstrating several multiplicity results of nontrivial weak solutions to double phase problems of Kirchhoff type with Hardy potentials.The main features of the paper are the appearance of no...This paper is devoted to demonstrating several multiplicity results of nontrivial weak solutions to double phase problems of Kirchhoff type with Hardy potentials.The main features of the paper are the appearance of non-local Kirchhoff coefficients and the Hardy potential,the absence of the compactness condition of Palais-Smale,and the L^(∞)-bound for any possible weak solution.To establish multiplicity results,we utilize the fountain theorem and the dual fountain theorem as main tools.Also,we give the L^(∞)-bound for any possible weak solution by exploiting the De Giorgi iteration method and a truncated energy technique.As an application,we give the existence of a sequence of infinitely many weak solutions converging to zero in L^(∞)-norm.To derive this result,we employ the modified functional method and the dual fountain theorem.展开更多
We consider a parametric double phase problem with a reaction term which is only locally defined near zero and is not assumed to be odd.We show that for all big values of the parameter λ,the problem has infinitely ma...We consider a parametric double phase problem with a reaction term which is only locally defined near zero and is not assumed to be odd.We show that for all big values of the parameter λ,the problem has infinitely many nodal solutions.Our approach is based on variational methods combining upper-lower solutions and truncation techniques,and flow invariance arguments.展开更多
The aim of this paper is the study of a double phase problems involving superlinear nonlinearities with a growth that need not satisfy the Ambrosetti-Rabinowitz condition.Using variational tools together with suitable...The aim of this paper is the study of a double phase problems involving superlinear nonlinearities with a growth that need not satisfy the Ambrosetti-Rabinowitz condition.Using variational tools together with suitable truncation and minimax techniques with Morse theory,the authors prove the existence of one and three nontrivial weak solutions,respectively.展开更多
文摘This paper is devoted to demonstrating several multiplicity results of nontrivial weak solutions to double phase problems of Kirchhoff type with Hardy potentials.The main features of the paper are the appearance of non-local Kirchhoff coefficients and the Hardy potential,the absence of the compactness condition of Palais-Smale,and the L^(∞)-bound for any possible weak solution.To establish multiplicity results,we utilize the fountain theorem and the dual fountain theorem as main tools.Also,we give the L^(∞)-bound for any possible weak solution by exploiting the De Giorgi iteration method and a truncated energy technique.As an application,we give the existence of a sequence of infinitely many weak solutions converging to zero in L^(∞)-norm.To derive this result,we employ the modified functional method and the dual fountain theorem.
基金Guangdong Basic and Applied Basic Research Foundation(2023A1515010603)。
文摘We consider a parametric double phase problem with a reaction term which is only locally defined near zero and is not assumed to be odd.We show that for all big values of the parameter λ,the problem has infinitely many nodal solutions.Our approach is based on variational methods combining upper-lower solutions and truncation techniques,and flow invariance arguments.
基金supported by the National Natural Science Foundation of China (No. 11201095)the Fundamental Research Funds for the Central Universities (No. 3072022TS2402)+1 种基金the Postdoctoral research startup foundation of Heilongjiang (No. LBH-Q14044)the Science Research Funds for Overseas Returned Chinese Scholars of Heilongjiang Province (No. LC201502)
文摘The aim of this paper is the study of a double phase problems involving superlinear nonlinearities with a growth that need not satisfy the Ambrosetti-Rabinowitz condition.Using variational tools together with suitable truncation and minimax techniques with Morse theory,the authors prove the existence of one and three nontrivial weak solutions,respectively.
