497 research outputs found

    Existence and Iteration of Positive Solutions for One-Dimensional p-Laplacian Boundary Value Problems with Dependence on the First-Order Derivative

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    This paper deals with the existence and iteration of positive solutions for the following one-dimensional p-Laplacian boundary value problems: (Õp(u′(t)))′+a(t)f(t,u(t),u′(t))=0, t∈(0,1), subject to some boundary conditions. By making use of monotone iterative technique, not only we obtain the existence of positive solutions for the problems, but also we establish iterative schemes for approximating the solutions

    Nontrivial Solutions for Asymmetric Kirchhoff Type Problems

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    We consider a class of particular Kirchhoff type problems with a right-hand side nonlinearity which exhibits an asymmetric growth at +∞ and −∞ in ℝN(N=2,3). Namely, it is 4-linear at −∞ and 4-superlinear at +∞. However, it need not satisfy the Ambrosetti-Rabinowitz condition on the positive semiaxis. Some existence results for nontrivial solution are established by combining Mountain Pass Theorem and a variant version of Mountain Pass Theorem with Moser-Trudinger inequality

    Infinitely many solutions for the p-fractional Kirchhoff equations with electromagnetic fields and critical nonlinearity

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    In this paper, we consider the fractional Kirchhoff equations with electromagnetic fields and critical nonlinearity. By means of the concentration-compactness principle in fractional Sobolev space and the Kajikiya's new version of the symmetric mountain pass lemma, we obtain the existence of infinitely many solutions, which tend to zero for suitable positive parameters

    Multiplicity of solutions for quasilinear elliptic equations with critical exponential growth

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    In this paper we consider a system of N-Laplacian elliptic equa- tions with critical exponential growth. The existence and multiplicity re- sults of solutions are obtained by a limit index method and Trudinger- Moser inequality
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