[PDF] Top 20 Existence and Boundedness of Solutions for Elliptic Equations in General Domains

... unbounded domains Guowei Dai By variational approach and the theory of the vari- able exponent Sobolev spaces establish the existence of infinitely many distinct homoclinic radially symmetric ... See full document

... It su ffi ces to show that { F y(r) | y ∈ Y } and { (F y) (r) | y ∈ Y } are uniformly bounded and equicontinuous on every subset [0,M] ⊂ [0, ∞ ). From (3.20), (3.21), the uniform boundedness is obvious, so we only ... See full document

... to general domains satisfying the “exterior measure” condition (A), and it works for both divergence and nondivergence ...for solutions in these two cases are ...of solutions, which are di ff ... See full document

... the existence or nonexistence of solutions; see [–] and the reference ...of solutions to problem (.) for more general nonlinear terms ... See full document

... the existence and uniqueness result for a more special sublinear system, and it was extended by Shi and Shivaji ...positive solutions of systems are radically symmetric and decreasing in radical direction ... See full document

... more general domains instead of the exterior domains, and second, we prove that λ ∗ is finite, and third, we also obtain the behavior of the two solutions on (0, λ ∗ ) and some bifurcation ... See full document

... of elliptic partial differential equations on Riemannian ...the existence and uniqueness of the positive finite energy radial solution to the equation H n u + λu + u p =  in ... See full document

... exists λ ∗ >  such that (.) has at least two nontrivial positive solutions for every λ ∈ (, λ ∗ ). Remark . We should mention that the above p-Laplacian problems studied in [, – ] are all not (p – ... See full document

... and existence of positive solutions for general nonlinear elliptic equations and systems, and that numerous related works are devoted to some of its variants, such as more ... See full document

... the existence of a W-solution of problem (P) (see ...a boundedness local result for such solution has been established in [2] under more restrictive hypotheses on data and weight ... See full document

... volving the p-Laplacian operator have been intensively studied in the last decades. We just remember the work on that topic of Jo˜ao Marcos B. do ´ O [7], Pfl¨uger [12], R˘adulescu and Smets [14] and the references ... See full document

... Dong, G: An existence theorem for weak solutions for a class of elliptic partial differential systems in general Orlicz-Sobolev spaces.. Fang, X, Yu, J: Solutions to operator equations on[r] ... See full document

... semilinear elliptic differential equations on bounded domains, Brezis and Lieb [] obtained an existence result of solutions for a class of elliptic equations with critical ... See full document

... the existence, the nonexistence, and the uniqueness of solutions of some special systems of nonlinear elliptic equations with boundary ... See full document

... Yang, “Existence of positive bounded entire solutions for quasilinear elliptic equations,” Ap- plied Mathematics and Computation , vol.. V´eron, “Local and global properties of solutions[r] ... See full document

... the existence of a positive ground state solution by using a constrained minimization ...the existence of a soliton solution for equation ...the existence of a ... See full document

... also be found in [2, 3, 6, 7, 12, 16], specially, in Deuel-Hess [10] for H 1 -solutions and in Brezis-Marcus-Ponce [4, 5] for L 1 -solutions when f is continuous and nondecreasing. In this paper, we extend ... See full document

... In this paper, we study the existence and multiplicity of coexistence states for an elliptic system modeling two subpopulations of the same species competing for resources. Our results generalize and ... See full document

... 3. Boundedness, Part 1. In this section, we obtain sufficient conditions for global existence in the future and for partial boundedness of the solutions of (1.1). To this end, in addition to ... See full document

... [7] C. Y. Liu, Z. P. Wang and H. S. Zhou, “Asymptotically Linear Schrödinger Equation with Potential Vanishing Atinfinity,” Journal of Differential Equations, Vol. 245, No. 1, 2008, pp. 201-222. ... See full document