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Existence and multiplicity results for some superlinear elliptic problems on RN
We study the semilinear elliptic PDE in RN The nonlinearity ƒ will be superlinear and subcritical. We prove the existence 0f a positive solution under various hypotheses on b. If and ƒ is odd in u,...
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Critical Point Theory on Partially Ordered Hilbert Spaces
We develop some abstract critical point theory in order to prove that boundary value problems like the model problem[formula] on a bounded domain Ω⊂RN, 2<p<2N/(N−2) have infinitely many sign changingExpand
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Infinitely Many Nonradial Solutions of a Euclidean Scalar Field Equation
Abstract We study the equation −Δu + b(|x|) u = ƒ(|x|, u), x ∈ R N ; u ∈ H 1 ( R N ). The existence of a nonradial solution has been an open problem for some time even in the autonomous case. UnderExpand
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Infinitely many solutions of a symmetric Dirichlet problem
Here Q is a bounded domain in [R” with smooth boundary and F: I?“’ + R is C’ and satisfies certain growth conditions. If m = 1 and F is an even function, hence, F,: R + R is an odd function, thenExpand
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Topological Methods for Variational Problems With Symmetries
Category, genus and critical point theory with symmetries.- Category and genus of infinite-dimensional representation spheres.- The length of G-spaces.- The length of representation spheres.- TheExpand
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On An Elliptic Equation With Concave and Convex Nonlinearities
We study the semilinear elliptic equation -Delta u=lambdau(q-2)u+muu(p-2)u in an open bounded domain Omega subset of R(N) with Dirichlet boundary conditions; here 1 0 and mu is an element of RExpand
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Partial symmetry of least energy nodal solutions to some variational problems
We investigate the symmetry properties of several radially symmetric minimization problems. The minimizers which we obtain are nodal solutions of superlinear elliptic problems, or eigenfunctions ofExpand
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Multiple positive solutions for a nonlinear Schrödinger equation
We are interested in positive entire solutions of the nonlinear Schrodinger equation \(-\Delta u+(\lambda a(x)+1)u = u^p\) where a? 0 has a potential well and p > 1 is subcritical. Using variationalExpand
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Multiple solutions of a critical polyharmonic equation
We prove that for N > 2m the equation (−∆)mu = |u| 4m N−2mu on RN has a sequence of nodal, finite energy solutions which is unbounded in Dm,2(RN ). This generalizes a classical result of Weiyue DingExpand
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