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      저자 : Kit Ian Kou (검색결과 2 건)
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      • KCI등재

        WEAK SOLUTIONS AND ENERGY ESTIMATES FOR A DEGENERATE NONLOCAL PROBLEM INVOLVING SUB-LINEAR NONLINEARITIES

        Jifeng Chu,Shapour Heidarkhani,Kit Ian Kou,Amjad Salari 대한수학회 2017 대한수학회지 Vol.54 No.5

        This paper deals with the existence and energy estimates of solutions for a class of degenerate nonlocal problems involving sub-linear nonlinearities, while the nonlinear part of the problem admits some hypotheses on the behavior at origin or perturbation property. In particular, for a precise localization of the parameter, the existence of a non-zero solution is established requiring the sublinearity of nonlinear part at origin and infinity. We also consider the existence of solutions for our problem under algebraic conditions with the classical Ambrosetti-Rabinowitz. In what follows, by combining two algebraic conditions on the nonlinear term which guarantees the existence of two solutions as well as applying the mountain pass theorem given by Pucci and Serrin, we establish the existence of the third solution for our problem. Moreover, concrete examples of applications are provided.

      • SCIESCOPUSKCI등재

        WEAK SOLUTIONS AND ENERGY ESTIMATES FOR A DEGENERATE NONLOCAL PROBLEM INVOLVING SUB-LINEAR NONLINEARITIES

        Chu, Jifeng,Heidarkhani, Shapour,Kou, Kit Ian,Salari, Amjad Korean Mathematical Society 2017 대한수학회지 Vol.54 No.5

        This paper deals with the existence and energy estimates of solutions for a class of degenerate nonlocal problems involving sub-linear nonlinearities, while the nonlinear part of the problem admits some hypotheses on the behavior at origin or perturbation property. In particular, for a precise localization of the parameter, the existence of a non-zero solution is established requiring the sublinearity of nonlinear part at origin and infinity. We also consider the existence of solutions for our problem under algebraic conditions with the classical Ambrosetti-Rabinowitz. In what follows, by combining two algebraic conditions on the nonlinear term which guarantees the existence of two solutions as well as applying the mountain pass theorem given by Pucci and Serrin, we establish the existence of the third solution for our problem. Moreover, concrete examples of applications are provided.

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