Department of Mathematics
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Item Existence of multiple solutions for a kirchho¤ type equation Involving polyharmonic operator with exponential growth(2020-08) Dwivedi, GauravIn this article, we establish the existence of three weak solutions for a nonlinear Kirchho¤ type elliptic equation involving polyharmonic operator by using variational methods. We assume that the nonlinearity satis es subcritical exponential growth condition. We use a critical point theorem by B. Ricceri to prove our result.Item Existence of solution to Kirchhoff type problem with gradient nonlinearity and a perturbation term(Springer, 2022-04) Dwivedi, GauravThis article deals with the existence of a weak solution to the Kirchhoff problem: where is a bounded and smooth domain in . We assume that f, h and A are continuous functions and the growth of the non linearity is dependent on u and . We do not assume any growth condition on the perturbation term h. In the case of we consider the exponential growth in the second variable of f. The proof of our main existence result uses an iterative technique based on the mountain pass theorem.Item Ground state solution to n-kirchhoff equation with critical exponential growth and without ambrosetti–rabinowitz condition(Springer, 2023-05) Dwivedi, GauravThis article is focused on the existence of a ground state solution to the Kirchhoff problem: where is a bounded domain with smooth boundary and . We assume that f satisfies critical exponential growth at infinity but does not satisfy the well-known Ambrosetti–Rabinowitz condition. We prove the existence of a ground state weak solution via mountain pass theorem and Nehari manifold technique.